2. A matrix is an ordered set of numbers listed in
rectangular form
Matrix A has 2 rows and 3 columns.
We say it is a 2x3 matrix.
order 2x3

3. B is a row matrix.
C is a column matrix.
This is the 3x3 zero-matrix.
I is the 3x3 Identity matrix.
and are opposite matrices.

4. We can sum matrices of the same order.
Multiplication of a matrix by a scalar
=3

5. To multiply matrices, we multiply rows into columns:
2 x 3 3x 2
=
2x 2
=
What special name has the answer?

6. Determinant of a matrix
Determinant of a matrix is a number calculated
from the elements of the matrix.
A =
det A=

7. Determinant of a 3x3 matrix

8. Find the determinant of:

9. If P= , find the value of x for which
|P| = 0.
If the determinant of a matrix is zero ,
the matrix is called a singular matrix

10. Inverse of a matrix
Only square matrices have inverses.
Not all square matrices have inverses.
matrix A has an inverse A­1
|A| ≠ 0
singular matrices have no inverse

11. 2x2 matrices:
or using GDC: x-1
key
3x3 matrices:
using GDC: x-1
key

12. Solutions of systems of linear equations
Using matrices we can rewrite these equations as:
A X = B
A­1
(AX) = A­1
B
(A­1
A) X = A­1
B
I X = A­1
B
X = A­1
B

13. X = A­1
BA X = B ⇒
X
⇒ x = 3 , y = 1

14. Given the simultaneous equations:
write them in matrix form and find x, y and z.

15. using GDC :

16. Use your GDC to find the inverse of the matrix
Hence, solve the simultaneous equations:
4 11 5
1 4 2
1 2 1
4 x + 11 y + 5 z = 2
x + 4 y + 2 z = 1
x + 2 y + 1 z = 4

17. The matrix A =
2 0 2
5 1 0
­1 4 a
a) Find an expression in terms of a for detA.
b) Find the value of a for which A-1
does not exist.
c) Solve the equation A when a = 0
giving your answers correct to 3 s.f.

18. Exercise Book page 336 Ex 1 a), 2 and 5
page 337 : EX8, 10,
revision exercise 12 page 339