Question

What is the product -4• [8,-1,-5,9]

Answer 1

The product of -4 and the vector
`\left[\begin{array}{c}8 \\-1 \\-5 \\9\end{array}\right]` is
`\left[\begin{array}{c}-32 \\4 \\20 \\-36\end{array}\right]`.

The product of a scalar and a vector involves multiplying each component of the vector by the scalar. In this case, the scalar is -4, and the vector is
`\left[\begin{array}{c}8 \\-1 \\-5 \\9\end{array}\right]`.

The product is obtained by multiplying each element of the vector by -4:

`-4 \cdot\left[\begin{array}{c}8 \\-1 \\-5 \\9\end{array}\right]=\left[\begin{array}{c}-4 \cdot 8 \\-4 \cdot(-1) \\-4 \cdot(-5) \\-4 \cdot 9\end{array}\right]=\left[\begin{array}{c}-32 \\4 \\20 \\-36\end{array}\right]`

So, the product is the vector
`\left[\begin{array}{c}-32 \\4 \\20 \\-36\end{array}\right]`

Answer 2

The product of given
`-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]` is
`\left[\begin{array}{ccc}-32 \\4\\20\\-36\end{array}\right]`

Explanation:

Consider the given product of a constant and a matrix.

`-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]`

To do product we multiply scalar -4 with each element of the matrix given,

`-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]= \left[\begin{array}{ccc}-4 * 8 \\-4 * -1\\-4 * -5\\-4 * 9\end{array}\right]`

On solving further , we get,

`\left[\begin{array}{ccc}-4 * 8 \\-4 * -1\\-4 * -5\\-4 * 9\end{array}\right]=\left[\begin{array}{ccc}-32 \\4\\20\\-36\end{array}\right]`

Thus, the product of given
`-4 \cdot \left[\begin{array}{ccc}8\\-1\\-5\\9\end{array}\right]` is
`\left[\begin{array}{ccc}-32 \\4\\20\\-36\end{array}\right]`