10. a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express each column vector of BA as a linear combination of the column vectors of B. In each part of Exercises 11-12, find matrices A, x, and b that express the given linear system as a single matrix equation Ax = b, and write out this matrix equation. 11. a. 2x₁ - 3x₂ + 5x3 = 7 9x1 - x₂ + x3 = -1 x₁ + 5x₂ + 4x3 = 0 - 3x3 + x4 = 1 5x₁ + x₂ − 8x = 3 X4 = 0 2x1 5x2 + 9x3 3x2x3 + 7x4 = 2 b. 4x1
10. a. Express each column vector of AB as a linear combination of the column vectors of A. b. Express each column vector of BA as a linear combination of the column vectors of B. In each part of Exercises 11-12, find matrices A, x, and b that express the given linear system as a single matrix equation Ax = b, and write out this matrix equation. 11. a. 2x₁ - 3x₂ + 5x3 = 7 9x1 - x₂ + x3 = -1 x₁ + 5x₂ + 4x3 = 0 - 3x3 + x4 = 1 5x₁ + x₂ − 8x = 3 X4 = 0 2x1 5x2 + 9x3 3x2x3 + 7x4 = 2 b. 4x1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 41E
Related questions
Question
(1.3)
Questions 10 and 11 on paper please thank you.
![c. (-AC)T + 5DT
d. (BAT-2C)T
e. BT(CCT-ATA)
f. DTET - (ED)T
In Exercises 7-8, use the following matrices and either the row
method or the column method, as appropriate, to find the indicated
row or column.
d
-2
7
6
2
4
A = 6
5
4
and B = 0
1
3
0
4
7
7.
a. the first row of AB
b. the third row of AB
c. the second column of AB d. the first column of BA
e. the third row of AA
f. the third column of AA
a. the first column of AB
b. the third column of BB
c. the second row of BB
d. the first column of AA
e. the third column of AB
f. the first row of BA
In Exercises 9-10, use matrices A and B from Exercises 7-8.
9. a. Express each column vector of AA as a linear combination
of the column vectors of A.
b. Express each column vector of BB as a linear combination
of the column vectors of B.
8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48922dd6-b6f8-4fac-84c6-05a7db5750f6%2F7a9b64ce-dd58-4024-aeb5-8596044be6d6%2Fp1fosrn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:c. (-AC)T + 5DT
d. (BAT-2C)T
e. BT(CCT-ATA)
f. DTET - (ED)T
In Exercises 7-8, use the following matrices and either the row
method or the column method, as appropriate, to find the indicated
row or column.
d
-2
7
6
2
4
A = 6
5
4
and B = 0
1
3
0
4
7
7.
a. the first row of AB
b. the third row of AB
c. the second column of AB d. the first column of BA
e. the third row of AA
f. the third column of AA
a. the first column of AB
b. the third column of BB
c. the second row of BB
d. the first column of AA
e. the third column of AB
f. the first row of BA
In Exercises 9-10, use matrices A and B from Exercises 7-8.
9. a. Express each column vector of AA as a linear combination
of the column vectors of A.
b. Express each column vector of BB as a linear combination
of the column vectors of B.
8.
![38
CHAPTER 1 Systems of Linear Equations and Matrices
10. a. Express each column vector of AB as a linear combination
of the column vectors of A.
b. Express each column vector of BA as a linear combination
of the column vectors of B.
In each part of Exercises 11-12, find matrices A, x, and b that express
the given linear system as a single matrix equation Ax = b, and
write out this matrix equation.
11. a. 2x₁ 3x₂ + 5x31 = 7
9x₁ - x₂ + x3 = -1
X₁ + 5x₂ + 4x3 =
0
- 3x3 +
x₁ =
= 1
5x₁ + x₂
− 8x = 3
X4 = 0
2x1 5x2 +9X3
3x₂x3 + 7x4 = 2
12. a. x₁2x2 + 3x3 = -3
b. 3x₁ + 3x₂ + 3x3 = -3
- 5x₂ - 2x3 = 3
2x₁ + x₂
=
0
-X1
- 3x₂ + 4x3
-
1
- 4x₂ + x3 = 0
X1
+ x3 =
5
In each part of Exercises 13-14, express the matrix equation as a sys-
tem of linear equations.
5
6
-7X₁
13. a.
-1
-2
3
X2
0
4 -1
X₂3
b. 4x₁](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48922dd6-b6f8-4fac-84c6-05a7db5750f6%2F7a9b64ce-dd58-4024-aeb5-8596044be6d6%2F77zmpxj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:38
CHAPTER 1 Systems of Linear Equations and Matrices
10. a. Express each column vector of AB as a linear combination
of the column vectors of A.
b. Express each column vector of BA as a linear combination
of the column vectors of B.
In each part of Exercises 11-12, find matrices A, x, and b that express
the given linear system as a single matrix equation Ax = b, and
write out this matrix equation.
11. a. 2x₁ 3x₂ + 5x31 = 7
9x₁ - x₂ + x3 = -1
X₁ + 5x₂ + 4x3 =
0
- 3x3 +
x₁ =
= 1
5x₁ + x₂
− 8x = 3
X4 = 0
2x1 5x2 +9X3
3x₂x3 + 7x4 = 2
12. a. x₁2x2 + 3x3 = -3
b. 3x₁ + 3x₂ + 3x3 = -3
- 5x₂ - 2x3 = 3
2x₁ + x₂
=
0
-X1
- 3x₂ + 4x3
-
1
- 4x₂ + x3 = 0
X1
+ x3 =
5
In each part of Exercises 13-14, express the matrix equation as a sys-
tem of linear equations.
5
6
-7X₁
13. a.
-1
-2
3
X2
0
4 -1
X₂3
b. 4x₁
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