Question

What is the product?

Answer 1

`\left[\begin{array}{ccc}-2\\0\\\end{array}\right]`

Explanation:

We have to find the product of a scalar and 2×2 matrix.

By finding the product of a scalar and a matrix ,we have to multiply the scalar by each entry of the matrix.

2.
`\left[\begin{array}{ccc}1\\4&\end{array}\right]`

`\left[\begin{array}{ccc}2.(-1)\\2.0\\\end{array}\right]`

`\left[\begin{array}{ccc}-2\\0\\\end{array}\right]` which is the product of a scalar and a matrix.

Answer 2

`\begin{bmatrix}-2\\0 \end{bmatrix}`

Explanation:

We have the product,
`2* \begin{bmatrix}-1\\0 \end{bmatrix}`.

It is known that,

'When we multiply a scalar with a matrix, the scalar is multiplied by each element of the matrix'.

So, we get,

`2* \begin{bmatrix}-1\\0 \end{bmatrix}`.

⇒
`\begin{bmatrix}-1* 2\\0* 2 \end{bmatrix}`

⇒
`\begin{bmatrix}-2\\0 \end{bmatrix}`

So, the resulting product is
`\begin{bmatrix}-2\\0 \end{bmatrix}`.