Directions:
Does the following inverse of [2 6 exist?
1 3]
If it isn't an inverse, explain why.
The inverse of a 2x2 matrix is given by:
A=[a b A^1=1/ad-bc[d -b
c d]. -c a].
If these two multiplied by each other gives the "identity matrix": [1 0
0 1].
then the inverse exists.
The determinant
|2 6|
|1 3| = 6-6 = 0
So, there is no inverse
To determine if the given matrix has an inverse, we need to calculate its determinant. The given matrix is:
[2 6]
[1 3]
First, let's calculate the determinant of the matrix by using the formula for a 2x2 matrix:
det(A) = (a * d) - (b * c)
Where a, b, c, and d are the elements of the matrix. In this case, a = 2, b = 6, c = 1, and d = 3. Substituting these values into the formula, we get:
det(A) = (2 * 3) - (6 * 1) = 6 - 6 = 0
The determinant of the matrix is 0.
If the determinant of a matrix is 0, it means that the matrix does not have an inverse. In this case, since the determinant of the given matrix is 0, the inverse of the matrix does not exist.
Therefore, the explanation is that the inverse does not exist because the determinant of the matrix is 0.