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- Question 3, Exercise 2.5
- 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 4, Exercise 2.6
- 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 5, Exercise 2.3
- 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
- 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
- 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
- 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.\\ $-x+3 y-5 z=0$\\ $2 x+
- Question 9 and 10, Exercise 2.6
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... 3 \beta$. ** Solution. ** =====Question 10===== By making use of matrix of order $2$ by $2$ and $3$ by $3$ encode and decode the following words:\\ a. PAKISTAN\\ b. ISLAMABAD\\ c. COLLEGE
- Question 1, Exercise 2.6
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... } So the system has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*} &\begin{ar... |A| = 0,$ the system has a non-trivial solution. By $(i)- 2(ii)$, we get: \begin{align*} &\begin{arra
- Question 4, Exercise 2.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... {cc} a & b \\ c & d \end{array}\right] $ is given by: \begin{align*} \left[\begin{array}{cc} a & b \
- Question 6, Exercise 2.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... beta \\ 3\beta & -3\beta \end{bmatrix}\end{align} By comparing corresponding elements in the matrices,
- Question 7, Exercise 2.2
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... 1 & 1 - 2(k + 1) \end{array}\right] \end{align*} By mathematical induction, the formula \[ A^n = \le
- Question 2, Exercise 2.6
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... {2} + 2x_{3} &= 0 \quad \text{(iii)} \end{align*} By using (i), we have \begin{align*} x_{1} &= 4x_{
- Question 1, Review Exercise
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo... tion having infinite many solutions can be solved by using: * (a) Inversion method * (b) Cr
- Question 1, Exercise 2.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo
- Question 2, Exercise 2.1
- el Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textboo