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
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
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