Let $A$ be the $2 \times 2$ matrices given by $A = [a_{i j}]$ where $a_{i j} = {0, 1, 2, 3, 4}$ such that $a_{11} + a_{12} + a_{21} + a_{22} = 4$
Find the number of matrices $A$ such that the trace of $A$ is equal to 4

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Solution

The correct option is C 5
Given $t r (A) = 4$
$\Rightarrow a_{11} + a_{22} = 4$
$a_{i j} = {0, 1, 2, 3, 4}$
So, diagonal entries of A can be 0 and 4 , 4 and 0, 1 and 3, 3 and 1, 2 and 2,
Hence, 5 matrices are possible

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Let A be the 2×2 matrices given by A=[aij] where aij={0,1,2,3,4} such that a11+a12+a21+a22=4Find the number of matrices A such that the trace of A is equal to 4

The correct option is C 5Given tr(A)=4⇒a11+a22=4aij={0,1,2,3,4}So, diagonal entries of A can be 0 and 4 , 4 and 0, 1 and 3, 3 and 1, 2 and 2,Hence, 5 matrices are possible

Let $A$ be the $2 \times 2$ matrices given by $A = [a_{i j}]$ where $a_{i j} = {0, 1, 2, 3, 4}$ such that $a_{11} + a_{12} + a_{21} + a_{22} = 4$
Find the number of matrices $A$ such that the trace of $A$ is equal to 4

The correct option is C 5
Given $t r (A) = 4$
$\Rightarrow a_{11} + a_{22} = 4$
$a_{i j} = {0, 1, 2, 3, 4}$
So, diagonal entries of A can be 0 and 4 , 4 and 0, 1 and 3, 3 and 1, 2 and 2,
Hence, 5 matrices are possible