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- Question 2, Exercise 2.3
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ===... 1 & 2 \\ 0 & 0 & 1 \end{matrix} \right. \right]\text{ by }R_1+3R_3\text{ and }R_2+2R_3 \\ \underset{\sim}{R}&\left[\begin{matrix} 1 & 4 & 14 \\ 0 & 5 & 6
- Question 1, Exercise 2.3
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... -1 \\ 0 & -5 & 6 \\ 0 & -5 & -2 \end{bmatrix} \text{ by } R_2-2R_1 \text{ and } R_3-3R_1 \\ \underset{\sim}{R}&\begin{bmatrix} 1 & 3 & -1 \\ 0 & -5 & 6 \
- Question 5, Exercise 2.2
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... & 2-3b+3b & 3-3c+3c \\ 4 & 5 & 6 \end{vmatrix} \text{ by } R_2-3R_1 \\ &=\begin{vmatrix} a & b & c \\... a & b & c\\ a+b+c & b+c+a & c+a+b \end{vmatrix} \text{ by } R_3+R_2 \\ &=(a+b+c)\begin{vmatrix} 1 & 1 &
- Question 3, Exercise 2.3
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... & -2 \\ 0 & 2 & 5 \\ 0 & 2 & 1 \end{bmatrix} \text{ by }R_2-2R_1 \text{ and } R_1-2R_3\\ \underset{\sim}{R}&\begin{bmatrix} 1 & 0 & -2 \\ 0 & 0 & 4 \\ 0
- Question 4, Exercise 2.3
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... 4 & 5 & 6 & 7 \\ 9 & 10 & 11 & 12 \end{bmatrix} \text{by}R_2-R_1\\ \underset{\sim}{R}&\begin{bmatrix} 1... 4 & 5 & 6 & 7 \\ 9 & 10 & 11 & 12 \end{bmatrix} \text{by}R_1\leftrightarrow R_2\\ \underset{\sim}{R}&\b
- Question 5 & 6, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... 1 \\ \end{matrix} \right]$$ This gives $$ 3a=-2 \text{ and } 2b=3,$$ $$\implies a=-\dfrac{2}{3} \text{ and } b=\dfrac{3}{2}.$$ =====Question 6(i)===== Solv
- Question 2, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... & 1 & 11 \end{bmatrix}\end{align} ====Go To==== <text align="left"><btn type="primary">[[ex2-1-p1 |< Question 1]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 3, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... (2), we have $$A(B-C)=AB-BC.$$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p2 |< Question 2]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 4, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. =... frac{1}{3}A^2-2A-9I=0 \end{align} ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p3 |< Question 3]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 7, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... (2), we have $(A+B)^t=A^t+B^t.$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p5 |< Question 5 & 6]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 8, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... trix} \right]$$ $$AA^t\ne A^tA$$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p6 |< Question 7]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 9, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... ght)}^{t}}={{B}^{t}}{{A}^{t}}$$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p7 |< Question 8]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 10, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... \right]$$ $$( A+B )^t=A^t+B^t$$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p8 |< Question 9]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 11, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... \right]$$ $$( A+B )^t=-( A+B )$$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p9 |< Question 10]]</btn></text> <text align="right"><btn type="success">[[math-1
- Question 12, Exercise 2.1
- 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. ==... ight]$$ $$( A-A^t )^t=-( A-A^t)$$ ====Go To==== <text align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p10 |< Question 11]]</btn></text> <text align="right"><btn type="success">[[math-1