If The matrix $$ x=\left(\begin{array}{ll}1 & 2 \ 3 & 4\end{array} ight) $$ and $$ y=\left(\begin{array}{ll}4 & 2 \ 1 & 3\end{array} ight. $$ find $$ 4 x-3 y $$

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If The matrix $$ x=\left(\begin{array}{ll}1 & 2 \ 3 & 4\end{array}ight) $$ and $$ y=\left(\begin{array}{ll}4 & 2 \ 1 & 3\end{array}ight. $$ find $$ 4 x-3 y $$

UpStudy AI · Accepted Answer

To find $$ 4x - 3y $$ where:

$$
x = \begin{pmatrix}
1 & 2 \
3 & 4
\end{pmatrix}, \quad
y = \begin{pmatrix}
4 & 2 \
1 & 3
\end{pmatrix}
$$

follow these steps:

### Step 1: Multiply Matrix $$ x $$ by 4

$$
4x = 4 \times \begin{pmatrix}
1 & 2 \
3 & 4
\end{pmatrix} = \begin{pmatrix}
4 \times 1 & 4 \times 2 \
4 \times 3 & 4 \times 4
\end{pmatrix} = \begin{pmatrix}
4 & 8 \
12 & 16
\end{pmatrix}
$$

### Step 2: Multiply Matrix $$ y $$ by 3

$$
3y = 3 \times \begin{pmatrix}
4 & 2 \
1 & 3
\end{pmatrix} = \begin{pmatrix}
3 \times 4 & 3 \times 2 \
3 \times 1 & 3 \times 3
\end{pmatrix} = \begin{pmatrix}
12 & 6 \
3 & 9
\end{pmatrix}
$$

### Step 3: Subtract $$ 3y $$ from $$ 4x $$

$$
4x - 3y = \begin{pmatrix}
4 & 8 \
12 & 16
\end{pmatrix} - \begin{pmatrix}
12 & 6 \
3 & 9
\end{pmatrix} = \begin{pmatrix}
4 - 12 & 8 - 6 \
12 - 3 & 16 - 9
\end{pmatrix} = \begin{pmatrix}
-8 & 2 \
9 & 7
\end{pmatrix}
$$

### Final Result

$$
4x - 3y = \begin{pmatrix}
-8 & 2 \
9 & 7
\end{pmatrix}
$$
$$ 4x - 3y = \begin{pmatrix} -8 & 2 \ 9 & 7 \end{pmatrix} $$

If The matrix \( x=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right) \) and \( y=\left(\begin{array}{ll}4 & 2 \\ 1 & 3\end{array}\right. \) find \( 4 x-3 y \)

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