select the correct answer. if $a = \\begin{bmatrix}5&-8\\3&0\\end{bmatrix}$ and $b = \\begin{bmatrix}2&-9\\1&…

select the correct answer. if $a = \\begin{bmatrix}5&-8\\3&0\\end{bmatrix}$ and $b = \\begin{bmatrix}2&-9\\1&0\\end{bmatrix}$, which matrix is the result of $2a - 3b$?\na. $\\begin{bmatrix}4&11\\3&0\\end{bmatrix}$\nb. $\\begin{bmatrix}4&38\\9&0\\end{bmatrix}$\nc. $\\begin{bmatrix}4&11\\9&0\\end{bmatrix}$\nd. $\\begin{bmatrix}1&-18\\1&0\\end{bmatrix}$

select the correct answer. if $a = \\begin{bmatrix}5&-8\\3&0\\end{bmatrix}$ and $b = \\begin{bmatrix}2&-9\\1&0\\end{bmatrix}$, which matrix is the result of $2a - 3b$?\na. $\\begin{bmatrix}4&11\\3&0\\end{bmatrix}$\nb. $\\begin{bmatrix}4&38\\9&0\\end{bmatrix}$\nc. $\\begin{bmatrix}4&11\\9&0\\end{bmatrix}$\nd. $\\begin{bmatrix}1&-18\\1&0\\end{bmatrix}$

Answer

Explanation:

Step1: Calculate 2A

Multiply each element of A by 2. [2A = 2\begin{bmatrix}5&-8\3&0\end{bmatrix}=\begin{bmatrix}2\times5&2\times(-8)\2\times3&2\times0\end{bmatrix}=\begin{bmatrix}10&-16\6&0\end{bmatrix}]

Step2: Calculate 3B

Multiply each element of B by 3. [3B = 3\begin{bmatrix}2&-9\1&0\end{bmatrix}=\begin{bmatrix}3\times2&3\times(-9)\3\times1&3\times0\end{bmatrix}=\begin{bmatrix}6&-27\3&0\end{bmatrix}]

Step3: Calculate 2A - 3B

Subtract corresponding elements of 3B from 2A. [2A - 3B=\begin{bmatrix}10 - 6&-16-(-27)\6 - 3&0 - 0\end{bmatrix}=\begin{bmatrix}4&11\3&0\end{bmatrix}]

Answer:

A. $\begin{bmatrix}4&11\3&0\end{bmatrix}$