Page 157 - Numerical Analysis Using MATLAB and Excel

Solutions to End−of−Chapter Exercises

)
5 × 1 + 9 × 5 + – ( 3 × 3 – ( 2 × 1 + 8 × 5 + 2 × 3 7 × 1 + – ( 4 × 5 + 6 × 3
)
)
⋅
BA = 5 × – ( 1 + 9 × 7 + – ( 3 × – ( 5 ) – ( 2 × – ( 1 + 8 × 7 + 2 × – ( 5 ) 7 × – ( 1 + – ( 4 × 7 + 6 × – ( 5 )
)
)
)
)
)
)
)
5 × – ( 4 + 9 × – ( 2 + – ( 3 × 6 – ( 2 × – ( 4 + 8 × – ( 2 + 2 × 6 7 × – ( 4 + – ( 4 × – ( 2 + 6 × 6
)
)
)
)
)
)
)
)
e.
41 73 – 56
= 44 48 4
5 – 65 16
f. CA⋅ not conformable for multiplication
)
)
)
)
)
)
⋅
DA = 1 × 1 + – ( 2 × 5 + 3 × 3 1 × – ( 1 + – ( 2 × 7 + 3 × – ( 5 ) 1 × – ( 4 + – ( 2 × – ( 2 + 3 × 6
)
)
)
)
)
)
– ( 3 × 1 + 6 × 5 + – ( 4 × 3 ( – 3 × – ( 1 + 6 × 7 + – ( 4 × – ( 5 ) – ( 3 × – ( 4 + 6 × – ( 2 + – ( 4 × 6
)
)
)
g.
= 0 – 30 18
–
15 65 24
)
)
)
h. DC⋅ = 1 × 4 + – ( 2 × – ( 3 + 3 × 5 1 × 6 + – ( 2 × 8 + 3 × – ( 2 ) = 25 – 16
)
)
)
– ( 3 × 4 + 6 × – ( 3 + – ( 4 × 5 – ( 3 × 6 + 6 × 8 + – ( 4 × – ( 2 ) – 50 38
)
)
3.
–
11 4 1 – 1
–
detA = 57 – 2 5 7
a. 35 63 – 5
–
)
)
)
)
)
)
)
= 1 × 7 × 6 + – ( 1 × – ( 2 × 3 + – ( 4 × 5 × – ( 5 – [ 3 × 7 × – ( 4 + – ( 5 × – ( 2 × 1 + 6 × 5 × – ( 1 ] )
)
)
= 42 + 6 + 100 – – ( 84 – 10 – – ( 30 = 252
5 9 3 5 9
–
detB = – 2 82 – 2 8
b. 7 – 4 6 7 – 4
)
)
)
)
)
)
= 5 × 8 × 6 + 9 × 2 × 7 + – ( 3 × – ( 2 × – ( 4 – [ 7 × 8 × – ( 3 + – ( 4 × 2 × 5 + 6 × – ( 2 × 9 ]
)
)
= 240 + 126 – 24 – – ( 168 + 40 – – ( 108 = 658
c. detC does not exist; matrix must be square
d. detD does not exist; matrix must be square
e. et A B⋅( ) = detA detB⋅ and from parts (a) and (b), det A B⋅( ) = 252 × 658 = 165816
f. det A C⋅( ) does not exist because detC does not exist
Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−39
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