Page 156 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

4.14 Solutions to End−of−Chapter Exercises

1.

1 + 5 – 1 + 9 – 4 – 3 6 8 – 7
a. A + B = 5 – 2 7 + 8 – 2 + 2 = 3 15 0 b. A + C not conformable for addition
3 + 7 – 5 – 4 6 + 6 10 – 9 12

c. B + D not conformable for addition d. C + D not conformable for addition

–
1 – 5 – 1 – 9 – 4 + 3 – 4 10 1
–
e. A – B = 5 + 2 7 – 8 – 2 – 2 = 7 – 1 – 4 f. A – C not conformable for subtraction
3 – 7 – 5 + 4 6 – 6 – 4 – 1 0

g. B – D not conformable for subtraction h. C – D not conformable for subtraction
2.

)
)
1 × 5 + – ( 1 × – ( 2 + – ( 4 × 7 1 × 9 + – ( 1 × 8 + – ( 4 × – ( 4 ) 1 × – ( 3 + – ( 1 × 2 + – ( 4 × 6
)
)
)
)
)
)
⋅
AB = 5 × 5 + 7 × – ( 2 + – ( 2 × 7 5 × 9 + 7 × 8 + – ( 2 × – ( 4 ) 5 × – ( 3 + 7 × 2 + – ( 2 × 6
)
)
)
)
)
)
)
)
3 × 5 + – ( 5 × – ( 2 + 6 × 7 3 × 9 + – ( 5) × 8 + 6 × – ( 4 ) 3 × – ( 3 + – ( 5 × 2 + 6 × 6
)
a.
– 21 17 – 29
= – 3 109 – 13
67 – 37 17
Check with MATLAB:
A=[1 −1 −4; 5 7 −2; 3 −5 6]; B=[5 9 −3; −2 8 2; 7 −4 6]; A*B
ans =
-21 17 -29
-3 109 -13
67 -37 17
×
)
)
)
×
)
)
1 4 + – ( 1 × – ( 3 + – ( 4 × 5 1 6 + – ( 1 × 8 + – ( 4 × – ( 2 ) – 13 6
b. A C⋅ = 5 4 +× 7 × – ( 3 + – ( 2 × 5 5 6 + 7 × 8 + – ( 2 × – ( 2 ) = – 11 90
×
)
)
)
)
×
)
×
3 4 +× – ( 5 × – ( 3 + 6 5 3 6 + – ( 5 × 8 + 6 × – ( 2 ) 57 – 34
)
⋅
c. BD not conformable for multiplication
)
×
41 6 ×+× – ( 3) 4 ( × – 2 + 66 43 6 ( × – 4 ) – 14 28 – 12
×
+
d. D⋅ = – ( 3 × 18 ( × – 3 ) – ( 3 × – ( 2 + 86 – ( 3 × 38 ( × – 4 ) = – 27 54 – 41
)
)
)
)
×
+
+
)
)
)
)
×
×
51 ( + – 2 × – ( 3 ) 5 ( × – 2 + – ( 2 × 6 53 ( + – 2 × – ( 4 ) 11 – 22 23
4−38 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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