Cambridge Additional Mathematics

310 Matrices (Chapter 12)

MATRIX SUBTRACTION

Suppose Thao’s stock levels were

0

@

29 51 19

31 28 32

40 17 29

1

Aand her sales matrix for the week was

0

@

15 12 6

20 16 19

19 8 14

1

A.

Thao will be left with her original stock levels less what she has sold. Clearly, we need to subtract

corresponding elements:

0

@

29 51 19

31 28 32

40 17 29

1

A¡

0

@

15 12 6

20 16 19

19 8 14

1

A=

0

@

14 39 13

11 12 13

21 9 15

1

A

Tosubtractmatrices, they must be of thesame order, and wesubtract

corresponding elements.

Summary:

Example 2 Self Tutor

If A=

μ

123

654

¶

, B=

μ

216

035

¶

, and C=

μ

31

24

¶

, find:

a A+B b A+C

a A+B=

μ

123

654

¶

+

μ

216

035

¶

=

μ

1+2 2+1 3+6

6+0 5+3 4+5

¶

=

μ

339

689

¶

b A+C cannot be found as the

matrices do not have the same

order.

Example 3 Self Tutor

If A=

0

@

348

210

147

1

Aand B=

0

@

206

304

523

1

A,

find A¡B.

A¡B=

0

@

348

210

147

1

A¡

0

@

206

304

523

1

A

=

0

@

3 ¡ 24 ¡ 08 ¡ 6

2 ¡ 31 ¡ 00 ¡ 4

1 ¡ 54 ¡ 27 ¡ 3

1

A

=

0

@

142

¡ 11 ¡ 4

¡42 4

1

A

² We can only add or subtract matrices of the same order.

² We add or subtract corresponding elements.

² The result of addition or subtraction is another matrix of the same order.

² A§B=(aij)§(bij)=(aij§bij)

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_12\310CamAdd_12.cdr Tuesday, 7 January 2014 5:56:06 PM BRIAN