Find A, B, AB, and |AB|. Then verify that |A||B| = |AB|. 1 3 -1 0 4 -3 A (a) (b) (c) 0 1 2 543 768 |A| |B| AB B 3 1 0 11

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.5: Other Types Of Equations
Problem 52E
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393-394

Find A, B, AB, and |AB|. Then verify that |A||B| = |AB|.
3
1
3
1 -1
[]
4
-3
A =
(a)
0 1 2
5 4 3
768
|A|
(b) |B|
(c) AB
(d) |AB|
7
B =
Transcribed Image Text:Find A, B, AB, and |AB|. Then verify that |A||B| = |AB|. 3 1 3 1 -1 [] 4 -3 A = (a) 0 1 2 5 4 3 768 |A| (b) |B| (c) AB (d) |AB| 7 B =
Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution.
X₁ + 2x₂ +
6x3
1
5x₁ + 5x₂ + 15x3
2
3x₁ + x₂ + 3x3 : = -7
The system has a unique solution because the determinant of the coefficient matrix is nonzero.
The system has a unique solution because the determinant of the coefficient matrix is zero.
The system does not have a unique solution because the determinant of the coefficient matrix is nonzero.
The system does not have a unique solution because the determinant of the coefficient matrix is zero.
=
Transcribed Image Text:Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. X₁ + 2x₂ + 6x3 1 5x₁ + 5x₂ + 15x3 2 3x₁ + x₂ + 3x3 : = -7 The system has a unique solution because the determinant of the coefficient matrix is nonzero. The system has a unique solution because the determinant of the coefficient matrix is zero. The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. The system does not have a unique solution because the determinant of the coefficient matrix is zero. =
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