Please answer the complex ones so I can get an understanding of how to do it. 1-5 0 0 |-21 05 | -50 -4 -3 ||70 1|3i.j.0 10 0|70 016 -2 |40 00 0 |10 06 | -51 -5 00 4 |-21 00 -3 |20 10 7 |9.k.1.0 12 |40 01 3 | 60 0 18 | -10 00 0 |13 -4-6 |50 1-30 |1 -2 -98 | -10 01 0 |-7(careful!)m.n.0 | 00 00 1 | 4|0 00 0 |10 -9 0 04 |710 0-53 |413 00 – 1|0 10 035|0.р.0 16 | -10 01 0-24 || -20 0 15 | 20 0 0 17-6 |3 Verify that the following augmented matrices are in rref, identify the leading and the freevariables, then find all the solutions, if there are any, to the systems of equationscorresponding to the rref. Assume that the variables are x1, x2,..., Xn. Use the letters r,s, t, and u for values of the free variables. Write your solutions in vector form.2.10 0 | -31 0 0 |70 10 | 2b.0 1 0 |а.0 0 1 | 60 0 1 |-41 -3 0 |7 | -30 1 -4 |1 02d.0 1 | -7с.0 0|0 0 | 01 -5 2 | 81 03 |0 0 | 0f.1 -2 0||6.е.0 0 | 00 00 1 | -41 0 0 -5 | 31 -9 03 | -5g.0 14 | 0h.0 1 -6 | 20 0 1 -7 | -20 0 0 |1

Answered: Image /qna-images/answer/526b7d66-ba1f-421e-83bf-0eb3cadffa17.jpg

Answered: 1 -5 0 0 | -2 1 0 0 7 5 | -5 0 1 0 | 3…

1 -5 0 0 | -2 1 0 0 7 5 | -5 0 1 0 | 3 j. 0 1 -4 -3 2 0 | 7 0 0 1 6 -2 | 4 0 0 0 | 1 0 0 6 | -5 1 -5 0 0 4 | -2 1 0 0 -3 1 0 7 | 9. 0 0 1 2 | 4 0 0 0 1 3 | | 6.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 36EQ

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.

Question

Please answer the complex ones so I can get an understanding of how to do it.

1
-5 0 0 |
-2
1 0
5 | -5
0 -4 -3 ||
7
0 1
|
3
i.
j.
0 1
0 0
|
7
0 0
1
6 -2 |
4
0 0
0 0 |
1
0 0
6 | -5
1 -5 0
0 4 |
-2
1 0
0 -3 |
2
0 1
0 7 |
9.
k.
1.
0 1
2 |
4
0 0
1 3 | 6
0 0 1
8 | -1
0 0
0 0 |
1
3 -4
-6 |
5
0 1
-3
0 |
1 -2 -9
8 | -1
0 0
1 0 |
-7
(careful!)
m.
n.
0 | 0
0 0
0 1 | 4
|
0 0
0 0 |
1
0 -9 0 0
4 |
7
1
0 0
-5
3 |
4
1
3 0
0 – 1
|
0 1
0 0
3
5
|
0.
р.
0 1
6 | -1
0 0
1 0
-2
4 |
| -2
0 0 1
5 | 2
0 0 0 1
7
-6 |
3

Verify that the following augmented matrices are in rref, identify the leading and the free
variables, then find all the solutions, if there are any, to the systems of equations
corresponding to the rref. Assume that the variables are x1, x2,..., Xn. Use the letters r,
s, t, and u for values of the free variables. Write your solutions in vector form.
2.
1
0 0 | -3
1 0 0 |
7
0 10 | 2
b.
0 1 0 |
а.
0 0 1 | 6
0 0 1 |-4
1 -3 0 |
7 | -3
0 1 -4 |
1 0
2
d.
0 1 | -7
с.
0 0
|
0 0 | 0
1 -5 2 | 8
1 0
3 |
0 0 | 0
f.
1 -2 0||
6.
е.
0 0 | 0
0 0
0 1 | -4
1 0 0 -5 | 3
1 -9 0
3 | -5
g.
0 1
4 | 0
h.
0 1 -6 | 2
0 0 1 -7 | -2
0 0 0 |
1

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