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