A is a 2 times 2 matrix such that A begin{bma | vedclass

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

Question

(D) Let $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$.Given $A \begin{bmatrix} 1 \ -1 \end{bmatrix} = \begin{bmatrix} -1 \ 2 \end{bmatrix}$,we

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) Let $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$.Given $A \begin{bmatrix} 1 \ -1 \end{bmatrix} = \begin{bmatrix} -1 \ 2 \end{bmatrix}$,we get:$a - b = -1$ $(1)$$c - d = 2$ $(2)$Given $A^2 \begin{bmatrix} 1 \ -1 \end{bmatrix} = \begin{bmatrix} 1 \ 0 \end{bmatrix}$,we can write this as $A \left( A \begin{bmatrix} 1 \ -1 \end{bmatrix} ight) = \begin{bmatrix} 1 \ 0 \end{bmatrix}$.Substituting $(1)$,we get $A \begin{bmatrix} -1 \ 2 \end{bmatrix} = \begin{bmatrix} 1 \ 0 \end{bmatrix}$.This gives the system:$-a + 2b = 1$ $(3)$$-c + 2d = 0$ $(4)$Solving $(1)$ and $(3)$: From $(1)$,$a = b - 1$. Substituting into $(3)$: $-(b - 1) + 2b = 1 \Rightarrow -b + 1 + 2b = 1 \Rightarrow b = 0$. Then $a = -1$.Solving $(2)$ and $(4)$: From $(2)$,$c = d + 2$. Substituting into $(4)$: $-(d + 2) + 2d = 0 \Rightarrow -d - 2 + 2d = 0 \Rightarrow d = 2$. Then $c = 4$.The matrix $A = \begin{bmatrix} -1 & 0 \ 4 & 2 \end{bmatrix}$.The sum of the elements is $a + b + c + d = -1 + 0 + 4 + 2 = 5$.

$A$ is a $2 \times 2$ matrix such that $A \begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} -1 \\ 2 \end{bmatrix}$ and $A^2 \begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$. The sum of the elements of $A$ is:

Similar Questions

Let $A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$ and $B = A^{20}$. Then the sum of the elements of the first column of $B$ is?

If $\begin{bmatrix} x+3 & z+4 & 2y-7 \\ -6 & a-1 & 0 \\ b-3 & -21 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 6 & 3y-2 \\ -6 & -3 & 2c+2 \\ 2b+4 & -21 & 0 \end{bmatrix}$,then find the values of $a, b, c, x, y$ and $z$.

If the matrix product $AB = O$,where $O$ is the null matrix,then which of the following is necessarily true?

If $A = \begin{bmatrix} 1 & -2 \\ 3 & 0 \end{bmatrix}$,$B = \begin{bmatrix} -1 & 4 \\ 2 & 3 \end{bmatrix}$,$C = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $5A - 3B - 2C = $

If $AB = C$,then the dimensions of matrices $A, B, C$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module