Determinants & Inverses (DP IB Applications & Interpretation (AI)) : Revision Note
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Determinants
What is a determinant?
The determinant is a numerical value (positive or negative) calculated from the elements in a matrix and is used to find the inverse of a matrix
You can only find the determinant of a square matrix
The method for finding the determinant of a
matrix is given in your formula booklet:
You only need to be able to find the determinant of a
matrix by hand
For larger
matrices you are expected to use your GDC
The determinant of an identity matrix is
The determinant of a zero matrix is
When finding the determinant of a multiple of a matrix or the product of two matrices:
(for a
matrix)
Worked Example
Consider the matrix , where
is a constant.
a) Given that , find the value of
.

b) Find the determinant of .

Inverse Matrices
How do I find the inverse of a matrix?
The determinant can be used to find out if a matrix is invertible or not:
If
, then
is invertible
If
, then
is singular and does not have an inverse
The method for finding the inverse of a
matrix is given in your formula booklet:
You only need to be able to find the inverse of a
matrix by hand
For larger
matrices you are expected to use your GDC
The inverse of a square matrix
is the matrix
such that the product of these matrices is an identity matrix,
As a result of this property:
(pre-multiplying by
)
(post-multiplying by
)
Worked Example
Consider the matrices ,
and
, where
is a constant.
a) Find .

b) Given that find the value of
.

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