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denis23 [38]
3 years ago
10

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

Mathematics
1 answer:
Whitepunk [10]3 years ago
6 0

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.

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