Question

Give an example of a 2x2 matrix whose determinant is 13.

Answer 1

Answer:

$\left[\begin{array}{ccc}1&0\\5&13\end{array}\right]$

Step-by-step explanation:

If we have a matrix 2x2 as:

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$

The determinant is given by:

determinant = a*d - b*c

So, for find a matrix whose determinant is 13, we can choose the values of a, b and c at random and then solve the equation for d.

Then, for example if we replace the value of a by 1 the value of b by 0, and the value of c by 5, the equation for find d could be:

determinant = a*d - b*c

13 = 1*d - 0*5

Solving for d, we get:

13 = d -0

13 = d

So, one example of a 2x2 matrix whose determinant is 13 is the matrix with the form:

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$

Where a is 1, b is 0, c is 5 and d is 13. This matrix is:

$\left[\begin{array}{ccc}1&0\\5&13\end{array}\right]$

Answer 2

If all your entries are integers, the determinant is also an integer. 
For this problem, 1        0
                             0        13

For this question, you should just fix  3 values and make the 4th value an unknown and solve it.
I hope my answer helped you somehow.