Question

consider the matrix equation:
$-2 \

$$\begin{bmatrix} 5 & 0 \\\\ 8 & -3 \\end{bmatrix}$$

+ \

$$\begin{bmatrix} 4 & 3 \\\\ 0 & -6 \\end{bmatrix}$$

= \

$$\begin{bmatrix} x_1 & x_2 \\\\ x_3 & x_4 \\end{bmatrix}$$

$.
what are the values of $x_1, x_2, x_3,$ and $x_4$?
note: your answers should be integers.
$x_1 = \square$
$x_2 = \square$
$x_3 = \square$
$x_4 = \square$

Explanation:

Step1: Multiply the first matrix by -2

To solve the matrix equation, we first perform the scalar multiplication on the first matrix. The scalar multiplication rule is that we multiply each element of the matrix by the scalar. So, for the matrix \(

$$\begin{bmatrix}5&0\\8&-3\end{bmatrix}$$

\), multiplying by -2 gives:

$$ -2
LATEXBLOCK1
=
LATEXBLOCK2
=
LATEXBLOCK3
$$

Step2: Add the two matrices

Next, we add the resulting matrix from Step 1 to the second matrix \(

$$\begin{bmatrix}4&3\\0&-6\end{bmatrix}$$

\). The rule for matrix addition is that we add the corresponding elements. So:

$$
LATEXBLOCK5
+
LATEXBLOCK6
=
LATEXBLOCK7
$$

Step3: Calculate each element

Now we calculate each element of the resulting matrix:

• For \(x_1\) (the element in the first row and first column): \(-10 + 4=-6\)
• For \(x_2\) (the element in the first row and second column): \(0 + 3 = 3\)
• For \(x_3\) (the element in the second row and first column): \(-16+0=-16\)
• For \(x_4\) (the element in the second row and second column): \(6+(-6)=0\)

Answer:

\(x_1=-6\), \(x_2 = 3\), \(x_3=-16\), \(x_4 = 0\)