Question

1. given the matrices a and b below, find a + b and 3a. (3 points)

a = \\(\

$$\begin{pmatrix}2&-3\\\\0&5\\\\7&-2\\end{pmatrix}$$

\\)
b = \\(\

$$\begin{pmatrix}1&0\\\\10&-1/2\\\\3&1\\end{pmatrix}$$

\\)

Explanation:

Step1: Find \(A + B\)

To add two matrices, add corresponding elements.
\[

$$\begin{align*} A + B&=\begin{pmatrix}2&- 3\\0&5\\7&-2\end{pmatrix}+\begin{pmatrix}1&0\\10&-\frac{1}{2}\\3&1\end{pmatrix}\\ &=\begin{pmatrix}2 + 1&-3+0\\0 + 10&5-\frac{1}{2}\\7+3&-2 + 1\end{pmatrix}\\ &=\begin{pmatrix}3&-3\\10&\frac{10 - 1}{2}\\10&-1\end{pmatrix}\\ &=\begin{pmatrix}3&-3\\10&\frac{9}{2}\\10&-1\end{pmatrix} \end{align*}$$

\]

Step2: Find \(3A\)

To multiply a matrix by a scalar, multiply each element by the scalar.
\[

$$\begin{align*} 3A&=3\begin{pmatrix}2&-3\\0&5\\7&-2\end{pmatrix}\\ &=\begin{pmatrix}3\times2&3\times(-3)\\3\times0&3\times5\\3\times7&3\times(-2)\end{pmatrix}\\ &=\begin{pmatrix}6&-9\\0&15\\21&-6\end{pmatrix} \end{align*}$$

\]

Answer:

\(A + B=

$$\begin{pmatrix}3&-3\\10&\frac{9}{2}\\10&-1\end{pmatrix}$$

\), \(3A=

$$\begin{pmatrix}6&-9\\0&15\\21&-6\end{pmatrix}$$

\)