Question

Select the correct answer. Which matrix represents this system of equations? -2y + 7z = 10 9x + 5y = 1 2x + z = -5

Answer 1

In matrix form this can be represented as

`\left[\begin{array}{ccc}0&-2&7\\0&5&0\\2&0&1\end{array}\right]`
`\left[\begin{array}{ccc}x\\y\\z\end{array}\right]` =
`\left[\begin{array}{ccc}10\\1\\5\end{array}\right]`



Explanation:

The given equations are

-2y + 7z = 10

9x + 5y = 1

2x + z = -5

Which can be written as

0x+-2y + 7z = 10

9x + 5y+0z = 1

2x +0y+ z = -5

In matrix form this can be represented as

`\left[\begin{array}{ccc}0&-2&7\\0&5&0\\2&0&1\end{array}\right]`
`\left[\begin{array}{ccc}x\\y\\z\end{array}\right]` =
`\left[\begin{array}{ccc}10\\1\\5\end{array}\right]`



When we multiply the above matrices we get the given set of equations.

In multiplying the matrices we check the no of columns of the first matrix and the number of rows of the second matrix. If they are equal ( as in this case they are 3) then the matrices can be multiplied .

The answer has the number of rows equal to the number of rows of the first matrix and the number of columns equal to the number of columns of the second matrix which is true in this case.