Question

Find all real values of a such that the given matrix is not invertible.

A= [0 9 a]
[a 1 7]
[0 a 1]

Answer 1

To find the values of a for which the given matrix is not invertible, we set the determinant equal to zero and solve for a.

Step-by-step explanation:

To determine the values of a for which the given matrix is not invertible, we need to find the values of a that result in a determinant of 0. The determinant of a matrix can be found using the formula:

determinant = (0 * (1 * 1) - a * (a * 1)) - (0 * (1 * 7) - 9 * (a * 1)) + (9 * (a * 7) - a * (0 * 1))

Setting the determinant equal to zero and solving for a will give us the values that make the matrix not invertible.

Answer 2

The answer is "0,3,-3".

Step-by-step explanation:

Let the matrix is not invertible.

then |A|=0

`\left|\begin{array}{ccc}0&9&a\\a&1&7\\0&a&1\end{array}\right|=0`

`-a[9-a^2]=0\\\\a=0\\\\a=\pm 3\\\\a=0, 3,-3\\`