Question

question 5 points 3

find -n if n = \

$$\begin{bmatrix} 1 & 15 & 16 & -12 & -32 \\\\ 13 & -14 & 24 & -15 & 50 \\\\ 60 & -16 & 17 & -5 & 20 \\\\ 2 & 9 & -11 & 6 & -50 \\\\ 10 & -40 & -10 & -20 & 60 \\end{bmatrix}$$

Explanation:

Understand the matrix negation operation

Using the Scalar Multiplication knowledge point

$$ -N = -1 \cdot N $$

Negate each element of the matrix

Using the Scalar Multiplication knowledge point

$$ N =
LATEXBLOCK0
$$

$$ -N =
LATEXBLOCK1
$$

Match with the given options

We compare our calculated matrix \(-N\) with the visible options:

• The first option has the last column as \([2, -2, -20, 50, -60]^T\), which is incorrect.
• The second option has the first three rows as:

$$
LATEXBLOCK2
$$

This matches our calculated matrix elements perfectly.

Answer:

• (A) \(

$$\begin{bmatrix} -1 & -15 & -16 & 12 & 2 \\ -13 & 14 & -24 & 15 & -2 \\ -60 & 16 & -17 & 5 & -20 \\ -2 & -9 & 11 & -6 & 50 \\ -10 & 40 & 10 & 20 & -60 \end{bmatrix}$$

\)

• **(B) \(

$$\begin{bmatrix} -1 & -15 & -16 & 12 & 32 \\ -13 & 14 & -24 & 15 & -50 \\ -60 & 16 & -17 & 5 & -20 \\ -2 & -9 & 11 & -6 & 50 \\ -10 & 40 & 10 & 20 & -60 \end{bmatrix}$$

\) (Correct answer)**