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- Question 4, Exercise 1.3 @math-11-nbf:sol:unit01
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... 3i \quad\cdots(2) \end{align} Multiplying Eq. (1) by $2$: \begin{align} &(2-2i)z+(2+2i) \omega=6 \quad \cdots (3) \end{align} Multiplying Eq. (2) by $(1-i)$: \begin{align} &2(1-i)z-(1-i) (2+5 i)\ome... i \quad \cdots(2) \end{align} Multiplying $(1)$ by $(1-2i)$, we get: \begin{align} &(1-2i)(2i z) +
- Question 3, Exercise 2.5 @math-11-nbf:sol:unit02
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ay}\right]$ if it exists. Also verify your answer by showing that $A A^{-1}=A^{-1} A=I$.\\ ** Solutio... & -1 & 1 & 0 & 0 \end{array} \right] \quad \text{by swapping } R1 \text{ and } R3\\ \sim&{\text{R}} \... & -1 & 1 & 0 & 0 \end{array} \right] \quad \text{by } R2 + R1 \\ \sim&{\text{R}} \left[ \begin{array}
- Question 8, Exercise 1.2 @math-11-nbf:sol:unit01
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... (i)==== Write $|2 z-i|=4$ in terms of $x$ and $y$ by taking $z=x+i y$. **Solution.** Given: $$|2z-i... Write $|z-1|=|\bar{z}+i|$ in terms of $x$ and $y$ by taking $z=x+i y$. **Solution.** Given: $$|z-1|=... rite $|z-4 i|+|z+4 i|=10$ in terms of $x$ and $y$ by taking $z=x+i y$. **Solution.** Given: $$|z-4i
- Question 4, Exercise 2.6 @math-11-nbf:sol:unit02
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ion 4(i)===== Solve the system of linear equation by Gauss-Jordan method.\\ $2 x_{1}-x_{2}-x_{3}=2$\\ ... n 4(ii)===== Solve the system of linear equation by Gauss-Jordan method.\\ $2 x_{1}-3 x_{2}+7 x_{3}=1... & 7 \end{bmatrix}\quad \text{(Divide } R_1 \text{ by 2)}\\ &\sim \text{R}\begin{bmatrix} 1 & -\frac{3}
- Question 1, Exercise 5.1 @math-11-nbf:sol:unit05
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... tan. =====Question 1(i)===== Find the remainder by using 'Remainder Theorem': $2 x^{3}+3 x^{2}-4 x+1$ is divided by $x+2$. ** Solution. ** Given: $p(x)=2 x^{3}+3 x^{2}-4 x+1$\\ $x-c=x+2 \implies c=-2$. By Remainder Theorem, we have \begin{align*} \text{R
- Definitions: Mathematics 11 NBF
- Textbook of Mathematics for Class XI is published by National Book Foundation (NBF), Islamabad, Pakist... 1$. Set of all complex numbers is usually denoted by $\mathbb{C}$. Every complex number $x+i y$ has tw... onjugate of a complex number $z=x+i y$ is denoted by $\bar{z}$ and is defined as $\bar{z}=x-i y$. **M... is a complex number, then its magnitude, denoted by $|z|$, is defined as $|z|=\sqrt{x^{2}+y^{2}}$. *
- Question 1, Exercise 1.3 @math-11-nbf:sol:unit01
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... z+\dfrac{3}{2}$ is the factor of polynomial. Then by using synthetic division: \begin{align} \begin{ar... So $z-(1)=z-1$ is the factor of polynomial. Then by using synthetic division: \begin{align} \begin{ar... So $z-(-3)=z+3$ is the factor of polynomial. Then by using synthetic division: Now, by synthetic divis
- Question 2, Exercise 1.3 @math-11-nbf:sol:unit01
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... istan. ====Question 2(i)==== Solve the equation by completing square: $z^{2}-6 z+2=0$. **Solution.*... }\}$. ====Question 2(ii)==== Solve the equation by completing square: $-\dfrac{1}{2} z^{2}-5 z+2=0$.... z^{2} - 5z + 2& = 0 \end{align} Multiply through by $-2$ to eliminate the fraction: \begin{align} z^2
- Question 5, Exercise 2.3 @math-11-nbf:sol:unit02
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ve inverse of the following matrices if it exists by adjoint method $\left[\begin{array}{ccc}1 & -1 & ... ve inverse of the following matrices if it exists by adjoint method $\left[\begin{array}{ccc}3 & -4 & ... ve inverse of the following matrices if it exists by adjoint method $\left[\begin{array}{ccc}i & 0 & 1
- Question 3, Exercise 2.6 @math-11-nbf:sol:unit02
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ion 3(i)===== Solve the system of linear equation by Gauss elimination method.\\ $2 x+3 y+4 z=2$\\ $2 ... on 3(ii)===== Solve the system of linear equation by Gauss elimination method.\\ $5 x-2 y+z=2$\\ $2 x+... n 3(iii)===== Solve the system of linear equation by Gauss elimination method.\\ $2 x+z=2$\\ $2 y-z=3$
- Question 5, Exercise 2.6 @math-11-nbf:sol:unit02
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... ion 5(i)===== Solve the system of linear equation by using Cramer's rule.\\ $x_{1}+x_{2}+2 x_{3}=8$\\ ... on 5(ii)===== Solve the system of linear equation by using Cramer's rule.\\ $2 x_{1}+2 x_{2}+x_{3}=0$\... n 5(iii)===== Solve the system of linear equation by using Cramer's rule.\\ $-2 x_{2}+3 x_{3}=1$\\ $3
- Question 6, Exercise 2.6 @math-11-nbf:sol:unit02
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... on 6(i)===== Solve the system of linear equation by matrix inversion method.FIXME\\ $5 x+3 y+z=6$\\ $... on 6(ii)===== Solve the system of linear equation by matrix inversion method.\\ $x+2 y-3 z=5$\\ $2 x-3... n 6(iii)===== Solve the system of linear equation by matrix inversion method.\\ $-x+3 y-5 z=0$\\ $2 x+
- Question 1 and 2, Exercise 5.2 @math-11-nbf:sol:unit05
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... mabad, Pakistan. =====Question 1===== Factorize by using factor theorem: $y^{3}-7 y-6$ ** Solution.... &=(-1)^{3}-7 (-1)-6 \\ &= -1+7-6 =0. \end{align*} By factor theorem, $y+1$ is factor of $f(y)$. Usin... align*} GOOD =====Question 2===== Factorize by using factor theorem: $2 x^{3}-x^{2}-2 x+1$ ** S
- Question 3 and 4, Exercise 5.2 @math-11-nbf:sol:unit05
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... mabad, Pakistan. =====Question 3===== Factorize by using factor theorem: $2 x^{3}+5 x^{2}-9 x-18$ *... - 18 \\ &= -16 + 20 + 18 - 18 = 0. \end{align*} By the factor theorem, \( x + 2 \) is a factor of \(... 2x - 3)(x + 3).$$ =====Question 4===== Factorize by using factor theorem: $3 x^{3}-5 x^{2}-36$ **Sol
- Question 5 and 6, Exercise 5.2 @math-11-nbf:sol:unit05
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... mabad, Pakistan. =====Question 5===== Factorize by using factor theorem: $t^{3}+t^{2}+3 t-5$ ** Sol... 1) - 5 \\ &= 1 + 1 + 3 - 5 \\ &= 0. \end{align*} By the factor theorem, \( t - 1 \) is a factor of \(... nd its other factors. **Solution.** It is given by the factor theorem, \( x - 2 \) is a factor of \(