Test the set of matrices for linear independence in M22. If it is linearly dependent, express one of the matrices as a linear combination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables A, B, C, and D as they relate to the question.) 0 2 -1 0 B = D = -2 2 -3 1 -1 7

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Test the set of matrices for linear independence in M22. If it is linearly dependent, express one of the matrices
as a linear combination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is
linearly dependent, enter your answer as an equation using the variables A, B, C, and D as they relate to the
question.)
0 2
D =
-1 0
-1 1
зо
A D
B =
C =
-2 2
-3 1
-1 7
Transcribed Image Text:Test the set of matrices for linear independence in M22. If it is linearly dependent, express one of the matrices as a linear combination of the others. (If the set is linearly independent, enter INDEPENDENT. If the set is linearly dependent, enter your answer as an equation using the variables A, B, C, and D as they relate to the question.) 0 2 D = -1 0 -1 1 зо A D B = C = -2 2 -3 1 -1 7
Row-reducing the augmented matrix gives the following result.
-1 3
1 0 0
-1
1 0
0 0
0 1 0
2
-2 1 -3 -1
0 0 1
2 1
7
0 0 0
Therefore, c, = t is a free variable with c,
])t, c2 = -t, and c, =
This tells us that there is --Select--
solution for this system and the matrices are linearly --Select--
--Select-
only a trivial
a non-trivial
1.
Transcribed Image Text:Row-reducing the augmented matrix gives the following result. -1 3 1 0 0 -1 1 0 0 0 0 1 0 2 -2 1 -3 -1 0 0 1 2 1 7 0 0 0 Therefore, c, = t is a free variable with c, ])t, c2 = -t, and c, = This tells us that there is --Select-- solution for this system and the matrices are linearly --Select-- --Select- only a trivial a non-trivial 1.
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