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- Question 1, Exercise 2.1
- slamabad, Pakistan. ===== Question 1(i) ===== Find the order of the following matrix $A=\left[\begin... times 3\end{align} ===== Question 1(ii) ===== Find the order of the following matrix $B=\left[\begin... = 3\times 2\end{align} ===== Question 1(iii)===== Find the order of the following matrix $C=\left[\begin... = 3\times 1\end{align} ===== Question 1(iv) ===== Find the order of the following matrix $D=\left[\begin
- Question 4, Exercise 2.1
- d, Islamabad, Pakistan. =====Question 4(i)===== Find the transpose of the following matrix and identif... & 6 & 9 \end{bmatrix}$$ =====Question 4(ii)===== Find the transpose of the following matrix and identif... \end{array}\right] $$ =====Question 4(iii)===== Find the transpose of the following matrix and identif... & 2 \end{array}\right]$$ =====Question 4(iv)===== Find the transpose of the following matrix and identif
- Question 4, Exercise 2.2
- d, Islamabad, Pakistan. =====Question 4(i)===== Find $A$ if \begin{align}\left[\begin{array}{cc} 2 & 1... y}\right]. \end{align*} =====Question 4(ii)===== Find $X$ if $$\begin{bmatrix}3 & 2 \\ 0 & 1 \\ 2 & 0\... t[\begin{array}{ll}2 & 14\end{array}\right]$ then find a non-zero matrix $C$ such that $A C=B C$. ** So... {array}{ll}8 & z \\ t & 6\end{array}\right]$ then find the values of $z, t$ and $x^{2}+y^{2}$. ** Solut
- Question 2, Exercise 2.3
- = 3\), \(a_{12} = 2\), and \(a_{13} = 3\). Now we find their corresponding cofactors. \begin{align*} A &... = -6 \end{align*} Now, we use these cofactors to find the determinant: \begin{align*} \det(A) &= a_{11}... 2\), \(a_{12} = 3\), and \(a_{13} = -1\). Now we find their corresponding cofactors. \begin{align*} A &... = -1 \end{align*} Now, we use these cofactors to find the determinant: \begin{align*} \det(A) &= a_{11}
- Question 5, Exercise 2.3
- d, Islamabad, Pakistan. =====Question 5(i)===== Find the multiplicative inverse of the following matri... $|A| = -9 \neq 0$, so $A$ is non-singular.\\ Let find the cofactor matrix for $A$.\\ \begin{align*} A_{... } \end{array}\right]$$ =====Question 5(ii)===== Find the multiplicative inverse of the following matri... ion. ** Do yourself. =====Question 5(iii)===== Find the multiplicative inverse of the following matri
- Question 3, Exercise 2.5
- estion 3(i)===== With the help of row operations, find the inverse of the matrix $\left[\begin{array}{cc... stion 3(ii)===== With the help of row operations, find the inverse of the matrix $\left[\begin{array}{cc... -6)\\ &=-2+19-3-19\neq 0 \end{align*} Now we will find $A^{-1}$ \begin{align*} &\quad\left[ \begin{array... tion 3(iii)===== With the help of row operations, find the inverse of the matrix $\left[\begin{array}{cc
- Question 4, Exercise 2.3
- d, Islamabad, Pakistan. =====Question 4(i)===== Find the value of $\lambda$, so that the given matrix ... ambda = \dfrac{16}{23}$. =====Question 4(ii)===== Find the value of $\lambda$, so that the given matrix ... = 4 \end{align*} =====Question 4(iii)===== Find the value of $\lambda$, so that the given matrix ... ution. ** Do yourself =====Question 4(iv)===== Find the value of $\lambda$, so that the given matrix
- Question 2, Exercise 2.5
- d, Islamabad, Pakistan. =====Question 2(i)===== Find the rank of each of the matrix $\left[\begin{arra... of the matrix is $3$. =====Question 2(ii)===== Find the rank of each of the matrix $\left[\begin{arra... of the matrix is $2$. =====Question 2(iii)===== Find the rank of each of the matrix $\left[\begin{arra... k of the matrix is $3$. =====Question 2(iv)===== Find the rank of each of the matrix $\left[\begin{arra
- Question 10, Exercise 2.2
- $ are two matrices such that $A B=B$ and $B A=A$. Find $A^{2}+B^{2}$ ** Solution. ** Given $$AB = B... e, given the conditions $AB = B$ and $BA = A$, we find that: $$A^2 + B^2 = A + B $$ ====Go to ==== <
- Question 6, Exercise 2.3
- \\ 0 & 1 & 0 \\ 2 & 1 & 6\end{array}\right]$ then find $A^{-1}$ and hence show that $A A^{-1}=A^{-1} A=I... & 0 \\ 2 & 1 & 6 \end{bmatrix} \end{align*} To find the inverse $ A^{-1} $ of the matrix $ A $, we wi
- Question 2, Exercise 2.6
- d, Islamabad, Pakistan. =====Question 2(i)===== Find the value of $\lambda$ for which the system of ho... \end{array} \right]$ =====Question 2(ii)===== Find the value of $\lambda$ for which the system of ho
- Question 6, Exercise 2.6
- 22 \end{align*} This system is consistent. Now to find $A^{-1}$, we calculate the cofactors of each elem... 0 \end{align*} This system is consistent. Now to find $A^{-1}$, we calculate the cofactors of each elem
- Question 7 and 8, Exercise 2.6
- 1 \\ 4 & -1 & 2 \\ 7 & 3 & -3\end{array}\right]$; find $A^{-1}$ and hence solve the system of equations.... q 0\end{align*} This system is consistent. Now to find $A^{-1}$, we calculate the cofactors of each elem
- Question 2 and 3, Review Exercise
- 0 \\ -3 & 4 & 9 \\ 2 & 1 & 6\end{array}\right]$; find $A_{13}, A_{23}$ and $A_{33}$; hence find $|A|$. ** Solution. ** Given: \begin{align*} A&=\left[\begi
- Question 1, Exercise 2.2
- iven \( a_{ij} = \frac{2i - 3j}{3} \), we need to find the matrix \( A \): \[ A = \begin{bmatrix} a_{11