Matrices

Answer

The matrix has 3 rows and 3 columns. Therefore, its order is $3 \times 3$.

Answer

Number of elements = number of rows × number of columns = $4 \times 3 = 12$. So, there are 12 elements.

Answer

We calculate each element: - $a_{11} = 1+1 = 2$ - $a_{12} = 1+2 = 3$ - $a_{13} = 1+3 = 4$ - $a_{21} = 2+1 = 3$ - $a_{22} = 2+2 = 4$ - $a_{23} = 2+3 = 5$ So, the matrix is: $$ \begin{bmatrix} 2 & 3 &…

Answer

This is a diagonal matrix because all non-diagonal elements are zero. Also, since all diagonal elements are equal and non-zero, it is a scalar matrix.

Answer

No. A scalar matrix must have equal non-zero elements on the diagonal. This is a zero matrix, not a scalar matrix.

Answer

Multiply each element by 3: $$ 3A = 3 \times \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} 3\cdot2 & 3\cdot3 \\ 3\cdot4 & 3\cdot5 \end{bmatrix} = \begin{bmatrix} 6 & 9 \\ 12 & 15 \en…

Answer

Add corresponding elements: $$ A + B = \begin{bmatrix} 1+5 & 2+6 \\ 3+7 & 4+8 \end{bmatrix} = \begin{bmatrix} 6 & 8 \\ 10 & 12 \end{bmatrix} $$…

Answer

No. Matrix addition is only defined when both matrices have the same order. A $2 \times 3$ matrix and a $3 \times 2$ matrix have different orders, so they cannot be added.