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Question 1, Exercise 2.1
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===== Question 1(i) ===== Find the order of the following matrix $A=\left[\begin{array}{lll}1 & 3 & 0 \\ 2 ... ===== Question 1(ii) ===== Find the order of the following matrix $B=\left[\begin{array}{ll}1 & 2 \\ 2 & 3 \... ===== Question 1(iii)===== Find the order of the following matrix $C=\left[\begin{array}{l}1 \\ 6 \\ 9\end{a... ===== Question 1(iv) ===== Find the order of the following matrix $D=\left[\begin{array}{llll}2 & 1 & 6 & 8\
Question 2, Exercise 2.1
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Pakistan. =====Question 1(i)===== Identify the following matrix $\quad A=\left[\begin{array}{lll}3 & 6 & 2... lar matrix =====Question 1(ii)===== Identify the following matrix $B=\left[\begin{array}{ll}\frac{1}{3} & 1 ... matrix =====Question 1(iii)===== Identify the following matrix $C=\left[\begin{array}{l}3 \\ 2 \\ 8\end{a... mn matrix =====Question 1(iv)===== Identify the following matrix $D=\left[\begin{array}{lll}1 & 6 & 9 \\ 2
Question 4, Exercise 2.1
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=====Question 4(i)===== Find the transpose of the following matrix and identify which one is symmetric and wh... ====Question 4(ii)===== Find the transpose of the following matrix and identify which one is symmetric and wh... ===Question 4(iii)===== Find the transpose of the following matrix and identify which one is symmetric and wh... ====Question 4(iv)===== Find the transpose of the following matrix and identify which one is symmetric and wh
Exercise 2.3 (Solutions)
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**Question. 1** Evaluate the determinant of the following matrices.\\ (i) $\left[\begin{array}{ccc}2 & 3 &... **Question. 2** Evaluate the determinants of the following matrices using cofactor method.\\ (i) $\left[\be... stion 2]] **Question. 3** Determine which of the following matrices are singular and which are non-singular.... stion. 5** Find the multiplicative inverse of the following matrices if it exists by adjoint method.\\ (i) $
Question 2, Exercise 2.3
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estion 2(i)===== Evaluate the determinant of the following matrix $\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & ... stion 2(ii)===== Evaluate the determinant of the following matrix $\left[\begin{array}{ccc}2 & 3 & -1 \\ -1 ... tion 2(iii)===== Evaluate the determinant of the following matrix $\left[\begin{array}{ccc}2 i & 6 & 1 \\ 1 ... stion 2(iv)===== Evaluate the determinant of the following matrix $\left[\begin{array}{ccc}1-i & 2 & 1+i \\
Exercise 2.1 (Solutions)
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of matrix. **Question 1.** Find the order of the following matrix:\\ (i) $A=\left[\begin{array}{lll}1 & 3 & ... ution: Question 1]] **Question 2.** Identify the following matrices as square matrix, rectangular matrix, ro... n 3]] **Question 4.** Find the transpose of the following matrices and identify which one of them are symme
Question 5, Exercise 2.3
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5(i)===== Find the multiplicative inverse of the following matrices if it exists by adjoint method $\left[\b... 5(ii)===== Find the multiplicative inverse of the following matrices if it exists by adjoint method $\left[\b... (iii)===== Find the multiplicative inverse of the following matrices if it exists by adjoint method $\left[\b
Question 7, Exercise 2.3
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fy that $(A B)^{-1}=B^{-1} A^{-1}$ in each of the following $A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 2 & -1 & ... fy that $(A B)^{-1}=B^{-1} A^{-1}$ in each of the following $A=\left[\begin{array}{ccc}2 & -i & 6 \\ 1 & 2 & ... fy that $(A B)^{-1}=B^{-1} A^{-1}$ in each of the following $A=\left[\begin{array}{ccc}1 & 2 & 5 \\ 1 & -1 &
Exercise 2.5 (Solutions)
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trices. **Question. 1** First reduce each of the following matrices into echelon form then into reduced eche... 1]] **Question. 2** Find the rank of each of the following matrices.\\ (i) $\left[\begin{array}{ccc}5 & 9 & ... e help of row operations, find the inverse of the following matrices if it exists.\\ Also verify your answer
Exercise 2.4 (Solutions)
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sing the properties of the determinants prove the following.\\ (i) $\left|\begin{array}{lll} x & y & x+y \\ y
Question 7 and 8, Exercise 2.6
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== Determine the value of $\lambda$ for which the following system has no solution, unique solution or infini
Question 9 and 10, Exercise 2.6
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r $2$ by $2$ and $3$ by $3$ encode and decode the following words:\\ a. PAKISTAN\\ b. ISLAMABAD\\ c. COLLEGE
Question 4 and 5, Review Exercise
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on 5===== Find the value of $\lambda$ so that the following system has infinite many solutions.\\ $2 x-3 y+z=
Review Exercise 2 (Solutions)
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tion 5.** Find the value of $\lambda$ so that the following system has infinite many solutions.\\ $2 x-3 y+z=