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I need to match them but I don't know how

I need to match them but I don't know how-example-1
User Caqu
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1 Answer

4 votes

Given:

The system of equations is:


x+3y=5


x-3y=-1

The given matrices are
\left[\begin{array}{cc}5&3\\-1&-3\end{array}\right],
\left[\begin{array}{cc}1&5\\1&-1\end{array}\right],
\left[\begin{array}{cc}1&3\\1&-3\end{array}\right].

To find:

The correct names for the given matrices.

Solution:

We have,


x+3y=5


x-3y=-1

Here, coefficients of x are 1 and 1 respectively, the coefficients of y are 3 and -3 respectively and constant terms are 5 and -1 respectively.

In the x-determinant, the coefficients of x are in the first column and the constant terms are in the second column. So, the x-determinant is:


\left[\begin{array}{cc}1&5\\1&-1\end{array}\right]

In the y-determinant, the constant terms are in the first column and the coefficients of y are in the second column. So, the y-determinant is:


\left[\begin{array}{cc}5&3\\-1&-3\end{array}\right]

In the system determinant, the coefficients of x are in the first column and the coefficients of y are in the second column. So, the system determinant is:


\left[\begin{array}{cc}1&3\\1&-3\end{array}\right]

Therefore, the first matrix is y-determinant, second matrix is x-determinant and the third matrix is the system determinant.

User Jack Valmadre
by
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