Write the given matrix equation as a system of linear equations without matrices. begin{bmatrix}3 & 0 -3 &1 end{bmatrix}begin{bmatrix}x y end{bmatrix}=begin{bmatrix}6 -7 end{bmatrix}

Question
Matrices
asked 2021-02-25
Write the given matrix equation as a system of linear equations without matrices. \(\begin{bmatrix}3 & 0 \\ -3 &1 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}6 \\-7 \end{bmatrix}\)

Answers (1)

2021-02-26
Step 1
Given: \(\begin{bmatrix}3 & 0 \\ -3 &1 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}6 \\-7 \end{bmatrix}\)
Step 2
Now, \(\begin{bmatrix}3 & 0 \\ -3 &1 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}6 \\-7 \end{bmatrix}\)
\(\therefore 3x+0\cdot y =6 \ \ \ \ \ \ \ (1)\)
\(-3x+1y =7 \ \ \ \ \ \ \ (2)\)
From equation (1) , we have
\(\Rightarrow 3x=6\)
\(\Rightarrow x=\frac{6}{3}\)
\(\Rightarrow x=3\)
Putting x=2 in equation (2) , we have
\(-3(2)+1y=7\)
\(\Rightarrow -6+y=7\)
\(\Rightarrow y=7+6\)
\(\Rightarrow y=13\)
Answer: Therefore the values of x and y are 2 and 13 respectively
0

Relevant Questions

asked 2021-02-05
Write the given matrix equation as a system of linear equations without matrices.
\(\begin{bmatrix}4 & -7 \\ 2 &-3 \end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix}=\begin{bmatrix}-3 \\1 \end{bmatrix}\)
asked 2021-02-09
Write the matrix equation as a system of linear equations without matrices.
\(\begin{bmatrix}2 & 0&-1 \\0 & 3&0\\1&1&0 \end{bmatrix}\begin{bmatrix}x \\ y \\z \end{bmatrix}=\begin{bmatrix}6 \\ 9\\5 \end{bmatrix}\)
asked 2021-02-26
Write the given matrix equation as a system of linear equations without matrices.
\(\begin{bmatrix}-1 & 0&1 \\ 0 & -1 &0 \\ 0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\ z \end{bmatrix}=\begin{bmatrix}-4 \\ 2 \\ 4 \end{bmatrix}\)
asked 2021-01-10
Write the matrix equation as a system of linear equations without matrices.
\(\begin{bmatrix}-1 & 0&1 \\0 & -1&0\\0&1&1 \end{bmatrix}\begin{bmatrix}x \\ y \\z \end{bmatrix}=\begin{bmatrix}-4 \\ 2\\4 \end{bmatrix}\)
asked 2020-12-22
The row echelon form of a system of linear equations is given.
(a) Write the system of equations corresponding to the given matrix.
Use x, y, or x, y, z, or \(x_1,x_2,x_3, x_4\)
(b) Determine whether the system is consistent. If it is consistent, give the solution.
\(\begin{matrix}1 & 0 & 3 & 0 &1 \\ 0 & 1 & 4 & 3&2\\0&0&1&2&3\\0&0&0&0&0 \end{matrix}\)
asked 2020-11-07
write B as a linear combination of the other matrices, if possible.
\(B=\begin{bmatrix}2 & 3 \\-4 & 2 \end{bmatrix} , A_1=\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 &-1 \\1 & 0 \end{bmatrix} , A_3=\begin{bmatrix}1 &1 \\0 & 1 \end{bmatrix}\)
asked 2021-01-15
write B as a linear combination of the other matrices, if possible.
\(B=\begin{bmatrix}2 & 5 \\0 & 3 \end{bmatrix} , A_1=\begin{bmatrix}1 & 2 \\-1 & 1 \end{bmatrix} , A_2=\begin{bmatrix}0 &1 \\2 & 1 \end{bmatrix}\)
asked 2021-01-31
The row echelon form of a system of linear equations is given.
(a) Write the system of equations corresponding to the given matrix.
Use x, y, or x, y, z, or \(x_1,x_2,x_3, x_4\)
(b) Determine whether the system is consistent. If it is consistent, give the solution.
\(\begin{matrix}1 & 0 & 2 & -1 \\ 0 & 1 & -4 & -2\\0&0&0&0&0 \end{matrix}\)
asked 2021-02-12
Write the given matrix equation as a system of linear equations without matrices.
\([(2,0,-1),(0,3,0),(1,1,0)][(x),(y),(z)]=[(6),(9),(5)]\)
asked 2021-01-30
Given the matrices
\(A=\begin{bmatrix}5 & 3 \\ -3 & -1 \\ -2 & -5 \end{bmatrix} \text{ and } B=\begin{bmatrix}0 & -2 \\ 1 & 3 \\ 4 & -3 \end{bmatrix}\)
find the 3x2 matrix X that is a solution of the equation. 2X-A=X+B
X=?
...