If A = begin{bmatrix} 1 & 2 & 3 5 & 0 & 7 6 | vedclass

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

Question

(C) The order of matrix $A$ is $3 	imes 3$ and the order of matrix $B$ is $2 	imes 3$.For matrix addition $A+B$,the orders must be identical,which i

Vedclass · Accepted Answer

$A'B'$

Vedclass · Answer

(C) The order of matrix $A$ is $3 	imes 3$ and the order of matrix $B$ is $2 	imes 3$.For matrix addition $A+B$,the orders must be identical,which is not the case here.For matrix multiplication $AB$,the number of columns in $A$ $(3)$ must equal the number of rows in $B$ $(2)$,which is not true.Now,consider the transpose matrices:$A'$ is of order $3 	imes 3$.$B'$ is of order $3 	imes 2$.For the product $A'B'$,the number of columns in $A'$ $(3)$ equals the number of rows in $B'$ $(3)$. Thus,$A'B'$ is defined.For the product $B'A'$,the number of columns in $B'$ $(2)$ must equal the number of rows in $A'$ $(3)$,which is not true.Therefore,the correct option is $C$.

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 5 & 0 & 7 \\ 6 & 2 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 5 \\ 0 & 0 & 2 \end{bmatrix}$,then which of the following is defined?

Similar Questions

Compute the indicated product: $\begin{bmatrix} a & b \\ -b & a \end{bmatrix} \begin{bmatrix} a & -b \\ b & a \end{bmatrix}$

If $A = \begin{bmatrix} 1 & 0 \\ 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 0 \\ 1 & 12 \end{bmatrix}$,then:

Let $A = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ and $B = \begin{bmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & -14^2 \\ -15^2 & 16^2 & 17^2 \end{bmatrix}$,then the value of $A^{\prime} BA$ is.

If $A = \begin{bmatrix} 1 & -2 & 1 \\ 2 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \end{bmatrix}$,then $(AB)^T$ is equal to

If $A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$,then prove that $A^n = \begin{bmatrix} 1+2n & -4n \\ n & 1-2n \end{bmatrix}$,where $n$ is any positive integer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module