Mathematics 9 (Complete Solutions)

# Q4 Multiply the following matrices.

(a)

 2 3 1 1 0 -2

 2 -1 3 0

(b)

 1 2 3 4 5 6

 1 2 3 4 -1 1

(c)

 1 2 3 4 -1 1

 1 2 3 4 5 6

(d)

 8 5 6 4

2
-
 5 2
-4 4

(e)

 -1 2 1 3

 0 0 0 0

Solution:

(a)

 2 3 1 1 0 -2

 2 -1 3 0

=

 2(2) + 3(3) 2(-1) + 3(0) 1(2) + 1(3) 1(-1) + 1(0) 0(2) + (-2)(3) 0(-1) + (-2)(0)

=

 4 + 9 -2 + 0 2 + 3 -1 + 0 0 - 6 0 + 0

=

 13 -2 5 -1 -6 0

(b)

 1 2 3 4 5 6

 1 2 3 4 -1 1

=

 1(1) + 2(3) + 3(-1) 1(2) + 2(4) + 3(1) 4(1) + 5(3) + 6(-1) 4(2) + 5(4) + 6(1)

=

 1 + 6 - 3 2 + 8 + 3 4 + 15 - 6 8 + 20 + 6

=

 4 13 13 34

(c)

 1 2 3 4 -1 1

 1 2 3 4 5 6

=

 1(1) + 2(4) 1(2) + 2(5) 1(3) + 2(6) 3(1) + 4(4) 3(2) + 4(5) 3(3) + 4(6) -1(1) + 1(4) -1(2) + 1(5) -1(3) + 1(6)

=

 1 + 8 2 + 10 3 + 12 3 + 16 6 + 20 9 + 24 -1 + 4 -2 + 5 -3 + 6

=

 9 12 15 19 26 33 3 3 3

(d)

 8 5 6 4

2
-
 5 2
-4 4

=

8(2) + 5(-4)
8( -
 5 2
) + 5(4)
6(2) + 4(-4)
6( -
 5 2
) + 4(4)

=

 16 - 20 -20 + 20 12 - 16 -15 + 16

=

 -4 0 -4 1

(e)

 -1 2 1 3

 0 0 0 0

=

 -1(0) + 2(0) -1(0) + 2(0) 1(0) + 3(0) 1(0) + 3(0)

=

 0 + 0 0 + 0 0 + 0 0 + 0

=

 0 0 0 0