ZedCar said:Homework Statement
What is the inverse of matrix A?
A=
(1) (2) (1)
(2) (-1) (2)
(1) (2) (1)
Homework Equations
The Attempt at a Solution
The determinant works out to be 0
The inverse is 1/determinant x adj(A)
Therefore the inverse is 1/0 x adj(A)
So is the answer to, what is the inverse, simply that it is undefined?
When the determinant of a matrix is 0, it means that the matrix is not invertible or singular. This means that the inverse of the matrix does not exist.
No, a matrix with a determinant of 0 does not have an inverse. The inverse of a matrix only exists when the determinant is non-zero.
To determine if a matrix has an inverse, you can calculate the determinant. If the determinant is 0, then the matrix does not have an inverse.
No, the inverse of a matrix with a determinant of 0 is not unique because the matrix does not have an inverse. A matrix must have a non-zero determinant to have a unique inverse.
Yes, a matrix with a determinant of 0 can still be used in calculations, but it cannot be inverted. This means that certain operations, such as finding the solution to a system of equations using the inverse matrix method, cannot be performed.