Question

Please solve the matrice​

Answer 1

AnswEr :

Given matrix,

$\sf A = \left[\begin{array}{c c c}2 & 1 & - 1 \\ 0 & 1 & - 2 \end{array} \right]_{2 \times 3}$

The above matrix is of the order 2 × 3,the order of the transpose would be 3 × 2

$\implies \sf A^t = \left[\begin{array}{c c }2 & 0 \\ 1 & 1 \\ -1 & - 2\end{array}\right]_{3 \times 2}$

Now,

$\sf{A^t \times A} \\ \\ \longrightarrow \ \left[\begin{array}{c c }2 & 0 \\ 1 & 1 \\ -1 & - 2\end{array}\right] \left[\begin{array}{c c c}2 & 1 & - 1 \\ 0 & 1 & - 2 \end{array}\right]\\ \\ \longrightarrow \left[\begin{array}{c c c}4 & 2 & -2 \\2 & 2 & -3 \\ -2& -3 & 3 \end{array}\right]_{3 \times 3}$

Here,the order of the matrix is 3 × 3

Also,

$\sf A \times A^t \\ \\ \longrightarrow \ \left[\begin{array}{c c c}2 & 1 & - 1 \\ 0 & 1 & - 2 \end{array}\right] \left[\begin{array}{c c }2 & 0 \\ 1 & 1 \\ -1 & - 2\end{array}\right] \\ \\ \longrightarrow \left[\begin{array}{c c } 6 & 3 \\ 5 & 5 \end{array}\right]_{2 \times 2}$

The order of the above matrix is 2 × 2

We notice that multiplication of matrices doesn't obey commutative law .