Find the inverse of the matrix,if it exists: | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $A = \left[\begin{array}{ll}2 & 1 \ 1 & 1\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2)(1) - (1)(1) = 2 - 1 = 1$.Since $

Vedclass · Accepted Answer

$A^{-1}=\left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight]$

Vedclass · Answer

(A) Let $A = \left[\begin{array}{ll}2 & 1 \ 1 & 1\end{array}ight]$.First,we find the determinant of $A$:$|A| = (2)(1) - (1)(1) = 2 - 1 = 1$.Since $|A| 
eq 0$,the inverse $A^{-1}$ exists.The inverse of a $2 	imes 2$ matrix $\left[\begin{array}{ll}a & b \ c & d\end{array}ight]$ is given by $\frac{1}{|A|} \left[\begin{array}{cc}d & -b \ -c & a\end{array}ight]$.Substituting the values $a=2, b=1, c=1, d=1$:$A^{-1} = \frac{1}{1} \left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight] = \left[\begin{array}{cc}1 & -1 \ -1 & 2\end{array}ight]$.

Find the inverse of the matrix,if it exists: $\left[\begin{array}{ll}2 & 1 \\ 1 & 1\end{array}\right]$

Similar Questions

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}$, $B = \operatorname{adj} A$ and $C = 5A$, then find the value of $\frac{|\operatorname{adj} B|}{|A|^4}$.

Assertion $(A)$: If $B$ is a $3 \times 3$ matrix and $|B|=6$,then $|\operatorname{Adj}(B)|=36$.
Reason $(R)$: If $B$ is a square matrix of order $n$,then $|\operatorname{Adj}(B)|=|B|^{n}$.

Matrix $A = \begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix}$. If $xyz = 60$ and $8x + 4y + 3z = 20$,then $A (adj A)$ is equal to:

Find the adjoint of the matrix: $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$

If $A$ is an invertible matrix of order $2$,then $\det(A^{-1})$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module