Question

If 3begin{bmatrix}x_1 & x_2 x_3 & x_4 end{bmatrix}=begin{bmatrix}x_1 & 2 -1 & 4x_4 end{bmatrix}+begin{bmatrix}4 & x_1+x_2 x_3+x_4 & 3 end{bmatrix} 1.

Matrices
ANSWERED
asked 2021-02-16
If \(3\begin{bmatrix}x_1 & x_2 \\x_3 & x_4 \end{bmatrix}=\begin{bmatrix}x_1 & 2 \\-1 & 4x_4 \end{bmatrix}+\begin{bmatrix}4 & x_1+x_2 \\x_3+x_4 & 3 \end{bmatrix}\)
1. \(x_1=-2 , x_2=2 , x_3=-2 , x_4=-3\)
2. \(x_1=2 , x_2=-2 , x_3=-2 , x_4=-3\)
3. \(x_1=2 , x_2=2 , x_3=2 , x_4=-3\)
4. \(x_1=2 , x_2=2 , x_3=-2 , x_4=3\)
5, \(x_1=2 , x_2=2 , x_3=-2 , x_4=-3\)

Answers (1)

2021-02-17
Step 1
We will perform the addition and scalar multiplication of matrices on both the sides.
Then we will compare corresponding elements in both matrices and will solve the equations.
Step 2
\(3\begin{bmatrix}x_1 & x_2 \\x_3 & x_4 \end{bmatrix}=\begin{bmatrix}x_1 & 2 \\-1 & 4x_4 \end{bmatrix}+\begin{bmatrix}3 & x_1+x_2 \\x_3+x_4 & 3 \end{bmatrix}\)
\(\therefore \begin{bmatrix}3x_1 & 3x_2 \\3x_3 & 3x_4 \end{bmatrix}=\begin{bmatrix}x_1+4 & 2+x_1+x_2 \\x_3+x_4-1 & 4x_4+3 \end{bmatrix}\)
\(\therefore 3x_1=x_1+4\)
\(2x_1=4\)
\(x_1=2\)
\(\therefore 3x_4=4x_4+3\)
\(x_4+3=0\)
\(x_4=-3\)
\(\therefore 3x_2=2+x_1+x_2\)
\(2x_2=2+x_1\)
\(2x_2=2+2\)
\(x_2=2\)
\(\therefore 3x_3=x_3+x_4-1\)
\(2x_3=x_4-1\)
\(=-3-1\)
\(x_3=-2\)
\(\therefore x_1=2,x_2=2,x_3=-2,x_4=-3\)
option 5
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