Question

let A be a 3 × 2 matrix and B be a 2×3 matrix .show that C=A.B is a singular matrix​

Answer 1

Answer:

Step-by-step explanation:

After multiplication of matrix AB ,then find determinant if value of determinant is equal to zero then we can say it's a singular matrix.

Answer 2

C = A . B is  a singular matrix.

Step-by-step explanation:

Given Data

A is a 3 × 2 matrix

B is a 2 × 3 matrix

To Prove that C = A.B is  a singular matrix

Let us consider, A = $\left[\begin{array}{cc}1&1&1&1 \\1&1\end{array}\right]$

And B = $\left[\begin{array}{ccc}1&1&1\\1&1&1\end{array}\right]$

A. B =    $\left[\begin{array}{cc}1&1&1&1 \\1&1\end{array}\right]$ .  $\left[\begin{array}{ccc}1&1&1\\1&1&1\end{array}\right]$

A. B = $\left[\begin{array}{ccc}2&2&2\\2&2&2\\2&2&2\end{array}\right]$

The matrix is said to be a singular matrix when its determinant is equals to zero .

Take determinant for the matrix A.B where A.B is equals to C

Determinant of C =  $\left[\begin{array}{ccc}2&2&2\\2&2&2\\2&2&2\end{array}\right]$

Determinant of C =   $2 \left[\begin{array}{ccc}2&2\\2&2\end{array}\right]$ - $2 \left[\begin{array}{ccc}2&2\\2&2\end{array}\right]$ + $2 \left[\begin{array}{ccc}2&2\\2&2\end{array}\right]$

Determinant of C = 2(4- 4) - 2(4-4) + 2(4-4)

Determinant of C = 2(0) -2(0) +2(0)

Determinant of C = 0 - 0 + 0

Determinant of C = 0

Therefore the matrix C = A.B is a singular matrix where their determinant is zero

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