Page 158 - Numerical Analysis Using MATLAB and Excel

Chapter 4 Matrices and Determinants

4.

1 – 2 11 2
–
Δ = – 2 3 1 2 3
–
34 – 5 34
)
)
)
)
)
= 1 × 3 × – ( 5 + – ( 2 × 1 × 3 + 1 × – ( 2 × 4 – [ 3 × 3 × 1 + 4 × 1 × 1 + – ( 5 × – ( 2 × – ( 2 ] )
= – 15 – 6 – 8 – 9 – 4 + 20 = – 22
– 4 2 14 2
–
–
D =
1 93 1 9 3
04 – 5 04
)
)
)
= – 4 × 3 × – ( 5 + – ( 2 × 1 × 0 + 1 × 9 × 4 – [ 0 × 3 × 1 + 4 × 1 × 4 + – ( 5 × 9 × – ( 2 ] )
= 60 + 0 + 36 – 0 + 16 – 90 = 22
1 – 4 11 4
–
D =
2 – 2 91 – 2 9
–
30 5 30
)
)
)
)
)
= 1 × 9 × – ( 5 + – ( 4 × 1 × 3 + 1 × – ( 2 × 0 – [ 3 × 9 × 1 + 0 × 1 × 1 + – ( 5 × – ( 2 × – ( 4 ] )
= – 45 – 12 – 0 – 27 – 0 + 40 = – 44
–
–
1 – 2 4 12
D =
3 – 2 39 – 2 3
340 3 4
)
)
)
)
)
= 1 × 3 × 0 + – ( 2 × 9 × 3 + – ( 4 × – ( 2 × 4 – [ 3 × 3 × – ( 4 + 4 × 9 × 1 + 0 × – ( 2 × – ( 2 ] )
= 0 – 54 + 32 + 36 – 36 – 0 = – 22
D D D
22
3
2
1
--------- =
x = ------- = --------- = – 1 x = ------- = – 44 2 x = ------- = – 22 1
--------- =
1
3
2
Δ
Δ
Δ
–
–
22
–
22
22
5.
x – 2x + x = – 4 (1)
3
1
2
– 2x + 3x + x = 9 (2)
1
3
2
3x + 4x – 5x = 0 (3)
2
3
1
Multiplication of (1) by yields
2
2x – 4x + 2x = – 8 (4)
2
1
3
Addition of (2) and (4) yields
– x + 3x = 1 (5)
2
3
4−40 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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