Question

Simplify 1)begin{bmatrix}4 & 5 end{bmatrix}+begin{bmatrix}6 & -4 end{bmatrix} 2)begin{bmatrix}4 & -13&3-5&-4 end{bmatrix}-begin{bmatrix}4 & -23&6-5&-6

Matrices
ANSWERED
asked 2021-02-11
Simplify
1)\(\begin{bmatrix}4 & 5 \end{bmatrix}+\begin{bmatrix}6 & -4 \end{bmatrix}\)
2)\(\begin{bmatrix}4 & -1\\3&3\\-5&-4 \end{bmatrix}-\begin{bmatrix}4 & -2\\3&6\\-5&-6 \end{bmatrix}\)
3)\(\begin{bmatrix}4 & -1\\6&-3 \end{bmatrix}+\begin{bmatrix}5 & -6\\5&-5 \end{bmatrix}-\begin{bmatrix}-2 & 0\\-2&-6 \end{bmatrix}\)
Solve for x and y
\(\begin{bmatrix}-10 & -4\\x&-1 \end{bmatrix}+\begin{bmatrix}-5 & 8\\y&-10 \end{bmatrix}=\begin{bmatrix}-15 & x\\16&-11 \end{bmatrix}\)

Answers (1)

2021-02-12
Step 1 To solve the given matrices. Step 2 Given that 1)\(\begin{bmatrix}4 & 5 \end{bmatrix}+\begin{bmatrix}6 & -4 \end{bmatrix}\)
\(\begin{bmatrix}4+6 & 5-4 \end{bmatrix}\)
\(\begin{bmatrix}10 & 1 \end{bmatrix}\)
\(\therefore \begin{bmatrix}4 & 5 \end{bmatrix}+\begin{bmatrix}6 & -4 \end{bmatrix}=\begin{bmatrix}10 & 1 \end{bmatrix}\)
2)\(\begin{bmatrix}4 & -1\\3&3\\-5&-4 \end{bmatrix}-\begin{bmatrix}4 & -2\\3&6\\-5&-6 \end{bmatrix}\)
\(\begin{bmatrix}4-4 & -1+2\\3-3&3-6\\-5+5&-4+6 \end{bmatrix}=\begin{bmatrix}0 & 1\\0&-3\\0&2 \end{bmatrix}\)
\(\therefore \begin{bmatrix}4 & -1\\3&3\\-5&-4 \end{bmatrix}-\begin{bmatrix}4 & -2\\3&6\\-5&-6 \end{bmatrix}=\begin{bmatrix}0 & 1\\0&-3\\0&2 \end{bmatrix}\)
3)\(\begin{bmatrix}4 & -1\\6&-3 \end{bmatrix}+\begin{bmatrix}5 & -6\\5&-5 \end{bmatrix}-\begin{bmatrix}-2 & 0\\-2&-6 \end{bmatrix}\)
\(\begin{bmatrix}4+5+2 & -1-6-0\\6+5+2&-3-5+6 \end{bmatrix}\)
\(\begin{bmatrix}3 & -5\\13&-2 \end{bmatrix}\)
\(\therefore \begin{bmatrix}4 & -1\\6&-3 \end{bmatrix}+\begin{bmatrix}5 & -6\\5&-5 \end{bmatrix}-\begin{bmatrix}-2 & 0\\-2&-6 \end{bmatrix}=\begin{bmatrix}3 & -5\\13&-2 \end{bmatrix}\)
Given that
\(\begin{bmatrix}-10 & -4\\x&-1 \end{bmatrix}+\begin{bmatrix}-5 & 8\\y&-10 \end{bmatrix}=\begin{bmatrix}-15 & x\\16&-11 \end{bmatrix}\)
\(\begin{bmatrix}-10-5 & -4+8\\x+y&-1-10 \end{bmatrix}=\begin{bmatrix}-15 & x\\16&-11 \end{bmatrix}\)
\(\begin{bmatrix}-15 & 4\\x+y&-11 \end{bmatrix}=\begin{bmatrix}-15 & x\\16&-11 \end{bmatrix}\)
Equating on both sides we have
x=4
x+y=16
Since x=4 then 4+y=16
y=12
\(\therefore x=4 \text{ and } y=12\)
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