Search
You can find the results of your search below.
Matching pagenames:
- Unit 01: Complex Numbers (Solutions)
- Unit 02: Matrices and Determinants (Solutions)
- Unit 04: Sequences and Seeries
- Unit 05: Polynomials
- Unit 08: Fundamental of Trigonometry
- Unit 09: Trigonometric Functions
- Question 1, Exercise 1.1
- Question 2, Exercise 1.1
- Question 3, Exercise 1.1
- Question 4, Exercise 1.1
- Question 5, Exercise 1.1
- Question 6, Exercise 1.1
- Question 7, Exercise 1.1
- Question 1, Exercise 1.2
- Question 2, Exercise 1.2
- Question 3, Exercise 1.2
- Question 4, Exercise 1.2
- Question 5, Exercise 1.2
- Question 6, Exercise 1.2
- Question 7, Exercise 1.2
- Question 8, Exercise 1.2
- Question 9, Exercise 1.2
- Question 10, Exercise 1.2
- Question 1, Exercise 1.3
- Question 2, Exercise 1.3
- Question 3, Exercise 1.3
- Question 4, Exercise 1.3
- Question 1, Exercise 1.4
- Question 2, Exercise 1.4
- Question 3, Exercise 1.4
- Question 4, Exercise 1.4
- Question 5, Exercise 1.4
- Question 6(i-ix), Exercise 1.4
- Question 6(x-xvii), Exercise 1.4
- Question 7, Exercise 1.4
- Question 8, Exercise 1.4
- Question 9, Exercise 1.4
- Question 10, Exercise 1.4
- Question 1, Review Exercise
- Question 2, Review Exercise
- Question 3, Review Exercise
- Question 4, Review Exercise
- Question 5, Review Exercise
- Question 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 1, Exercise 2.1
- Question 2, Exercise 2.1
- Question 3, Exercise 2.1
- Question 4, Exercise 2.1
- Question 1, Exercise 2.2
- Question 3, Exercise 2.2
- Question 3, Exercise 2.2
- Question 4, Exercise 2.2
- Question 5, Exercise 2.2
- Question 6, Exercise 2.2
- Question 7, Exercise 2.2
- Question 8, Exercise 2.2
- Question 9, Exercise 2.2
- Question 10, Exercise 2.2
- Question 11, Exercise 2.2
- Question 12, Exercise 2.2
- Question 13, Exercise 2.2
- Question 1, Exercise 2.3
- Question 2, Exercise 2.3
- Question 3, Exercise 2.3
- Question 4, Exercise 2.3
- Question 5, Exercise 2.3
- Question 6, Exercise 2.3
- Question 7, Exercise 2.3
- Question 1, Exercise 2.5
- Question 2, Exercise 2.5
- Question 3, Exercise 2.5
- Question 1, Exercise 2.6
- Question 2, Exercise 2.6
- Question 3, Exercise 2.6
- Question 4, Exercise 2.6
- Question 5, Exercise 2.6
- Question 6, Exercise 2.6
- Question 7 and 8, Exercise 2.6
- Question 9 and 10, Exercise 2.6
- Question 1, Review Exercise
- Question 2 and 3, Review Exercise
- Question 4 and 5, Review Exercise
- Question 1 and 2, Exercise 4.1
- Question 3 and 4, Exercise 4.1
- Question 5 and 6, Exercise 4.1
- Question 7 and 8, Exercise 4.1
- Question 9 and 10, Exercise 4.1
- Question 11 and 12, Exercise 4.1
- Question 13 and 14, Exercise 4.1
- Question 15 and 16, Exercise 4.1
- Question 17 and 18, Exercise 4.1
- Question 19 and 20, Exercise 4.1
- Question 21 and 22, Exercise 4.1
- Question 1, Exercise 4.2
- Question 2, Exercise 4.2
- Question 3 and 4, Exercise 4.2
- Question 5 and 6, Exercise 4.2
- Question 7 and 8, Exercise 4.2
- Question 9 and 10, Exercise 4.2
- Question 11 and 12, Exercise 4.2
- Question 13, Exercise 4.2
- Question 14 and 15, Exercise 4.2
- Question 16 and 17, Exercise 4.2
- Question 1 and 2, Exercise 4.3
- Question 3 and 4, Exercise 4.3
- Question 5 and 6, Exercise 4.3
- Question 7 and 8, Exercise 4.3
- Question 9 and 10, Exercise 4.3
- Question 11 and 12, Exercise 4.3
- Question 13 and 14, Exercise 4.3
- Question 15 and 16, Exercise 4.3
- Question 17, 18 and 19, Exercise 4.3
- Question 20, 21 and 22, Exercise 4.3
- Question 23 and 24, Exercise 4.3
- Question 25 and 26, Exercise 4.3
- Question 1 and 2, Exercise 4.4
- Question 3 and 4, Exercise 4.4
- Question 5, 6 and 7, Exercise 4.4
- Question 8 and 9, Exercise 4.4
- Question 10 and 11, Exercise 4.4
- Question 12 and 13, Exercise 4.4
- Question 14 and 15, Exercise 4.4
- Question 16 and 17, Exercise 4.4
- Question 18 and 19, Exercise 4.4
- Question 20 and 21, Exercise 4.4
- Question 22 and 23, Exercise 4.4
- Question 24 and 25, Exercise 4.4
- Question 26 and 27, Exercise 4.4
- Question 28 and 29, Exercise 4.4
- Question 30, Exercise 4.4
- Question 1 and 2, Exercise 4.5
- Question 3 and 4, Exercise 4.5
- Question 5 and 6, Exercise 4.5
- Question 7 and 8, Exercise 4.5
- Question 9 and 10, Exercise 4.5
- Question 11, 12 and 13, Exercise 4.5
- Question 14, Exercise 4.5
- Question 15, Exercise 4.5
- Question 16, Exercise 4.5
- Question 1 and 2, Exercise 4.6
- Question 3 & 4, Exercise 4.6
- Question 5 & 6, Exercise 4.6
- Question 7 & 8, Exercise 4.6
- Question 9 & 10, Exercise 4.6
- Question 11, Exercise 4.6
- Question 12, Exercise 4.6
- Question 1 and 2, Exercise 4.7
- Question 3 and 4, Exercise 4.7
- Question 5 and 6, Exercise 4.7
- Question 7 and 8, Exercise 4.7
- Question 9 and 10, Exercise 4.7
- Question 11, 12 and 13, Exercise 4.7
- Question 14, 15 and 16, Exercise 4.7
- Question 17 and 18, Exercise 4.7
- Question 19 and 20, Exercise 4.7
- Question 19 and 20, Exercise 4.7
- Question 21 and 22, Exercise 4.7
- Question 23 and 24, Exercise 4.7
- Question 25 and 26, Exercise 4.7
- Question 27 and 28, Exercise 4.7
- Question 29 and 30, Exercise 4.7
- Question 1 and 2, Exercise 4.8
- Question 3 and 4, Exercise 4.8
- Question 5 and 6, Exercise 4.8
- Question 7 and 8, Exercise 4.8
- Question 9 and 10, Exercise 4.8
- Question 11 and 12, Exercise 4.8
- Question 13, 14 and 15, Exercise 4.8
- Question 1, Exercise 5.1
- Question 2 and 3, Exercise 5.1
- Question 4 and 5, Exercise 5.1
- Question 6 and 7, Exercise 5.1
- Question 8 and 9, Exercise 5.1
- Question 10, Exercise 5.1
- Question 1 and 2, Exercise 5.2
- Question 3 and 4, Exercise 5.2
- Question 5 and 6, Exercise 5.2
- Question 7 and 8, Exercise 5.2
- Question 1, Exercise 5.3
- Question 2, Exercise 5.3
- Question 3, Exercise 5.3
- Question 4, Exercise 5.3
- Question 5, Exercise 5.3
- Question 6, Exercise 5.3
- Question 2, Review Exercise
- Question 1, Review Exercise
- Question 2 & 3, Review Exercise
- Question 4 & 5, Review Exercise
- Question 6 & 7, Review Exercise
- Question 8, Review Exercise
- Question 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 1, Exercise 8.1
- Question 2, Exercise 8.1
- Question 3, Exercise 8.1
- Question 4, Exercise 8.1
- Question 5 and 6, Exercise 8.1
- Question 7, Exercise 8.1
- Question 8, Exercise 8.1
- Question 9, Exercise 8.1
- Question 10, Exercise 8.1
- Question 11, Exercise 8.1
- Question 12, Exercise 8.1
- Question 13, Exercise 8.1
- Question 14, Exercise 8.1
- Question 1, 2 and 3 Exercise 8.2
- Question 4 Exercise 8.2
- Question 5 Exercise 8.2
- Question 6 Exercise 8.2
- Question 7 Exercise 8.2
- Question 8(i, ii & iii) Exercise 8.2
- Question 8(iv, v & vi) Exercise 8.2
- Question 8(vii, viii & ix) Exercise 8.2
- Question 8(x, xi & xii) Exercise 8.2
- Question 8(xiii, xiv & xv) Exercise 8.2
- Question 8(xvi, xvii & xviii) Exercise 8.2
- Question 8(xix, xx, xxi & xxii) Exercise 8.2
- Question 1(i, ii, iii & iv) Exercise 8.3
- Question 1(v, vi, vii & viii) Exercise 8.3
- Question 1(ix, x & xi) Exercise 8.3
- Question 2(i, ii, iii, iv and v) Exercise 8.3
- Question 3(i, ii, iii, iv & v) Exercise 8.3
- Question 3(vi, vii, viii, ix & x) Exercise 8.3
- Question 3(xi, xii & xiii) Exercise 8.3
- Question 4 Exercise 8.3
- Question 1, Review Exercise
- Question 2, Review Exercise
- Question 3, Review Exercise
- Question 4, Review Exercise
- Question 5 and 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 9, Review Exercise
- Question 10, Review Exercise
- Question 1, Exercise 9.1
- Question 2, Exercise 9.1
- Question 3, Exercise 9.1
- Question 4(i-iv), Exercise 9.1
- Question 4(v-viii), Exercise 9.1
- Question 5(i-v), Exercise 9.1
- Question 5(vi-x), Exercise 9.1
- Question 6, Exercise 9.1
- Question 7 & 8, Exercise 9.1
- Question 9, Exercise 9.1
- Question 10, Exercise 9.1
- Question 2 and 3,Review Exercise
- Question 4, Review Exercise
- Question 1,Review Exercise
- Question 2 and 3, Review Exercise
- Question 4, Review Exercise
- Question 5 and 6, Review Exercise
- Question 7, Review Exercise
- Question 8, Review Exercise
- Question 9, Review Exercise
- Question 10(i-v), Review Exercise
- Question 10(vi-x), Review Exercise
- Question 10(xi-xv), Review Exercise
Fulltext results:
- Unit 04: Sequences and Seeries
- ult" title="Exercise 4.1 (Solutions)"> * [[math-11-nbf:sol:unit04:ex4-1-p1|Question 1 & 2]] * [[math-11-nbf:sol:unit04:ex4-1-p2|Question 3 & 4]] * [[math-11-nbf:sol:unit04:ex4-1-p3|Question 5 & 6]] * [[math-11-nbf:sol:unit04:ex4-1-p4|Question 7 & 8]] * [[ma
- Unit 08: Fundamental of Trigonometry
- t 08: Fundamental of Trigonometry ====== {{ :math-11-nbf:sol:math-11-nbf-unit-08.jpg?nolink&477x400|Unit 08: Fundamental of Trigonometry}} This is a eight... ult" title="Exercise 8.1 (Solutions)"> * [[math-11-nbf:sol:unit08:ex8-1-p1|Question 1]] * [[math-11-nbf:sol:unit08:ex8-1-p2|Question 2 ]] * [[math-1
- Unit 01: Complex Numbers (Solutions)
- it 01: Complex Numbers (Solutions) ===== {{ :math-11-nbf:sol:math-11-nbf-sol-unit01.jpg?nolink&400x335|Unit 01: Complex Numbers (Solutions)}} This is a fi... ult" title="Exercise 1.1 (Solutions)"> * [[math-11-nbf:sol:unit01:ex1-1-p1|Question 1]] * [[math-11-nbf:sol:unit01:ex1-1-p2|Question 2]] * [[math-11
- Unit 02: Matrices and Determinants (Solutions)
- ult" title="Exercise 2.1 (Solutions)"> * [[math-11-nbf:sol:unit02:ex2-1-p1|Question 1]] * [[math-11-nbf:sol:unit02:ex2-1-p2|Question 2]] * [[math-11-nbf:sol:unit02:ex2-1-p3|Question 3]] * [[math-11-nbf:sol:unit02:ex2-1-p4|Question 4]] </panel> <pan
- Question 6, Exercise 2.6 @math-11-nbf:sol:unit02
- he cofactors of each element . \begin{align*} A_{11} &= (-1)^{1+1} \left| \begin{array}{cc} 1 & 3 \\ ... ay} \right| = 5 - 6 = -1\\ A&= \begin{bmatrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\... ix}\\ \implies A^{-1} &= \begin{bmatrix} \frac{1}{11} & \frac{5}{11} & \frac{-4}{11} \\ \frac{5}{22} & \frac{-19}{22} & \frac{18}{22} \\ \frac{-3}{22} & \
- Unit 05: Polynomials
- ====== Unit 05: Polynomials ====== {{ :math-11-nbf:sol:math-11-nbf-unit-05.jpg?nolink|Unit 05: Polynomials}} This is a fifth unit of the book "Model... ult" title="Exercise 5.1 (Solutions)"> * [[math-11-nbf:sol:unit05:ex5-1-p1|Question 1]] * [[math-11-nbf:sol:unit05:ex5-1-p2|Question 2 & 3]] * [[mat
- Question 8, Exercise 2.2 @math-11-nbf:sol:unit02
- ). Let \begin{align*} A &= \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix}\\ B &= \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \\ b_{31} & b_{32} \end{bmatrix}\\ AB &= \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \\ b_{31} & b_{32}
- Unit 09: Trigonometric Functions
- ult" title="Exercise 9.1 (Solutions)"> * [[math-11-nbf:sol:unit09:ex9-1-p1|Question 1]] * [[math-11-nbf:sol:unit09:ex9-1-p2|Question 2 ]] * [[math-11-nbf:sol:unit09:ex9-1-p3|Question 3]] * [[math-11-nbf:sol:unit09:ex9-1-p4|Question 4(i-iv)]] * [[m
- Question 2, Exercise 2.3 @math-11-nbf:sol:unit02
- ** Solution. ** The elements of \(R_1\) are \(a_{11} = 3\), \(a_{12} = 2\), and \(a_{13} = 3\). Now w... 4 & 5 & 1 \\ 2 & 1 & 0 \end{array}\right]\\ & A_{11} = (-1)^{1+1} \left|\begin{array}{cc} 5 & 1 \\ 1 ... ind the determinant: \begin{align*} \det(A) &= a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13} \\ &= 3(-1) + 2(2) + 3(-6) \\ &= -3 + 4 - 18 \\ &= -17 \end{a
- Question 1, Exercise 1.3 @math-11-nbf:sol:unit01
- n.** \begin{align} & 3z^2 + 363 \\ = & 3(z^2 - (11i)^2)\\ = & 3(z + 11i)(z - 11i) \end{align} ====Question 1(iv)==== Factorize the polynomial into linear functions: $z^{2}... olynomial into linear functions: $2 z^{3}+9 z^{2}-11 z-30$. **Solution.** Suppose $$P(z)=2z^3 + 9z^2
- Question 9, Exercise 2.2 @math-11-nbf:sol:unit02
- ** Let: \begin{align*} A &= \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \... a_{33} \end{pmatrix} \\ B &= \begin{pmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \... gn*} \begin{align*} A + B &= \begin{pmatrix} a_{11} + b_{11} & a_{12} + b_{12} & a_{13} + b_{13} \\ a_{21} + b_{21} & a_{22} + b_{22} & a_{23} + b_{23}
- Question 4, Exercise 2.6 @math-11-nbf:sol:unit02
- frac{3}{2} & \frac{7}{2} & : & \frac{1}{2} \\ 0 & 11 & -17 & : & 2 \\ 10 & -4 & 18 & : & 7 \end{bmatri... frac{3}{2} & \frac{7}{2} & : & \frac{1}{2} \\ 0 & 11 & -17 & : & 2 0 & 11 & -17 & : & 2 \end{bmatrix}\quad \text{(} R_3 \text{ - 10}R_1)\\ &\sim \text{R}... rac{7}{2} & : & \frac{1}{2} \\ 0 & 1 & -\frac{17}{11} & : & \frac{2}{11} \\ 0 & 0 & 0 & : & 0 \end{bma
- Question 2, Exercise 4.2 @math-11-nbf:sol:unit04
- he next three terms of each arithmetic sequence. $11,14,17, \ldots$ ** Solution. ** Given: $$11, 14, 17, \ldots$$ Thus $a_1=11$, $d=14-11=3$.\\ Now $$a_n=a_1+(n-1)d.$$ So, we have \begin{align*} a_4 &= 11 + (4-1) \cdot 3 = 11 +
- Question 7, Review Exercise @math-11-nbf:sol:unit01
- ===== Solve by completing square method $2 z^{2}-11 z+16=0$. ** Solution. ** \begin{align*} &2 z^{2}-11 z+16=0\\ \implies&z^2 - \dfrac{11}{2}z + 8 = 0\\ \implies& z^2 - \dfrac{11}{2}z = -8\\ \implies& z^2 - 2z\dfrac{11}{4}z + \dfrac{121}{1
- Question 2, Exercise 2.6 @math-11-nbf:sol:unit02
- \right|=0\\ &2(12-2)+\lambda(8+3)+1(-4-9)=0\\ &20+11\lambda-13=0\\ &\lambda =-\frac{7}{11}\\ \end{align*} The system becomes \begin{align*} &2 x_{1}+ \frac{7}{11}x_{2}+x_{3}=0 \cdots(iv)\\ &2 x_{1}+3 x_{2}-x_{3}... begin{align*} &\begin{array}{cccc} 2x_1&+\frac{7}{11} x_{2}&+ x_{3}&=0\\ \mathop+\limits_{-}2x_1&\ma