Question

Find the determinant and state whether the matrix has an inverse.

Answer 1

Answers:

• determinant = 4
• the matrix inverse does exist

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Step-by-step explanation:

When given this template 2x2 matrix

`\begin{bmatrix}a&b\\c&d\end{bmatrix}`

The determinant is a*d-b*c

We multiply the diagonal entries, then subtract the products. This applies to 2x2 matrices only.

In this case we have:

• a = 13
• b = 3
• c = 16
• d = 4

So this particular determinant is:

a*d - b*c = 13*4 - 3*16 = 52 - 48 = 4

The determinant is 4

The nonzero determinant tells us that the matrix inverse does exist.

If the determinant was zero, then the matrix inverse would not exist. This is because the inverse involves the factor
`\frac{1}{\text{determinant}}`. Recall that dividing by zero is not allowed.