5 Questions
What is the determinant of matrix $A$?
-1
Which equation corresponds to the following matrix equation: $\begin{bmatrix} 5 & 3 \ 2 & 1 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} -1 \ -8 \end{bmatrix}$?
$5x + 3y = -1$ and $2x + y = -8$
What is the value of the determinant $d(A)$ given $d(A) = \begin{vmatrix} 5 & -3 \ 2 & 1 \end{vmatrix}$?
11
In the given system of equations, what does the matrix $B$ represent?
$\begin{bmatrix} -1 \ -8 \end{bmatrix}$
What is the value of the determinant $|A|$ when calculated using the elements $5$, $3$, $2$, and $1$?
-1
Study Notes
Matrices and Linear Equations
- The system of linear equations is represented as: $5x + 3y = -1$ and $2x + y = -8$
- The above system can be represented in matrix form as: $\begin{bmatrix} 5 & 3 \ 2 & 1\end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} -1 \ -8 \end{bmatrix}$
- The matrix equation can be written in compact form as: $\frac{\begin{bmatrix} 5 & 3 \ 2 & 1 \end{bmatrix}}{A} \frac{\begin{bmatrix} x \ y \end{bmatrix}}{x} = \frac{\begin{bmatrix} -1 \ -8 \end{bmatrix}}{B}$
- The determinant of matrix A is: $|A| = \begin{vmatrix} 5 & 3 \ 2 & 1 \end{vmatrix} = -1$
- The determinant of matrix A for x is: $d(A) = \begin{vmatrix} 5 & -3 \ 2 & 1 \end{vmatrix} = 11$
Solve a system of linear equations using matrices and determinants. Find the values of x and y.
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