Question

If possible , find 2A-4BA=begin{bmatrix}-3 & 5 & -6 3 & -5 & -1 end{bmatrix} , B=begin{bmatrix}-6 & 8 & -3 3 & 6 & -2 end{bmatrix}a. begin{bmatrix}-30 & 42 & -24 18 & 14 & -10 end{bmatrix}

Matrices
ANSWERED
asked 2021-01-10

If possible , find \(2A-4B\)
\(A=\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix} , B=\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}\)
a. \(\begin{bmatrix}-30 & 42 & -24 \\ 18 & 14 & -10 \end{bmatrix}\)
b. not possible
c. \(\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}\)
d. \(\begin{bmatrix} -9 & 13 & -9 \\ 6 & 1 & -3 \end{bmatrix}\)
c. \(\begin{bmatrix} 18 & -22 & 0 \\ -6 & -34 & 6 \end{bmatrix}\)

Expert Answers (1)

2021-01-11

Step 1
Consider the given matrices,
Since, the order of the matrix A is \(2 \times 3\)(2 rows and 3 columns) and also order of the matrix B is \(2 \times 3\)
Here, the order of the matrix A and B is same.
So, subtraction of matrix \(2A -4B\) is possible.
Step 2
Now, find \(2A -4B\).
\(A=\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix} , B=\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}\)
Now , \(2A-4B=2\begin{bmatrix}-3 & 5 & -6 \\ 3 & -5 & -1 \end{bmatrix}-4\begin{bmatrix}-6 & 8 & -3 \\ 3 & 6 & -2 \end{bmatrix}\)
Multiply 2 and 4 every element of matrix A and B respectively.
\(= \begin{bmatrix}-6 & 10 & -12 \\ 6 & -10 & -2 \end{bmatrix}-\begin{bmatrix}-24 & 32 & -12 \\ 12 & 24 & -8 \end{bmatrix}\)
\(= \begin{bmatrix}-6-(-24) & 10-32 & -12-(-12) \\ 6-12 & -10-24 & -2-(-8) \end{bmatrix}\)
\(= \begin{bmatrix} -6+24 & -22 & -12+12 \\ -6 & -34 & -2+8 \end{bmatrix}\)
\(= \begin{bmatrix} 18 & -22 & 0 \\ -6 & -34 & -6 \end{bmatrix}\)

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