A matrix has an inverse if and only if its determinant is not zero.
& - 4/9 & & -1/9 & & 7/18 & & 2/9 &
Practice makes perfect
To find the inverse of the given 2* 2 matrix, we will use the corresponding formula.
Matrix
Inverse
A= [ cc a & b c & d ]
A^(- 1)=1/ad-bc [ cc d & - b - c & a ] where ad-bc ≠0
The expression ad-bc is known as the determinant of a 2* 2 matrix. Because it is in the denominator of a fraction, if the determinant is zero, the matrix cannot have an inverse. Consider the given matrix.
[
cc
-4 & -2 7 & 8
]
Let's calculate its determinant.
Since the determinant is not zero, the matrix has an inverse. We can now apply the formula for the inverse. Note that we usually refer to the determinant using the notation ad-bc=det(A).
