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Since the matrices are linearly dependent we must now express one of the matrices as a linear combination of the others. We first recall the given set of matrices. 0 2 D = -1 1 3 0 -1 B = 2. C = 1 -з 1 -2 Next, recall the previously created matrix equation and substitute the variables A, B, C, and D in place of the matrices. -1 1 3 0 + c, + Ca -3 1 -1 0 + C. -1 = 0 7 -2 2 CA + czB + c3C + cD = 0 Finally, substitute c, = -4t, c, = -t, c, = 2t, and c, = t into the matrix equation. %3! %3D CA + c„B + c3C + cD = 0 ):)A + (-t)8 + (( De)c + (t)D = 0

Since the matrices are linearly dependent we must now express one of the matrices as a linear combination of the others. We first recall the given set of matrices. 0 2 D = -1 1 3 0 -1 B = 2. C = 1 -з 1 -2 Next, recall the previously created matrix equation and substitute the variables A, B, C, and D in place of the matrices. -1 1 3 0 + c, + Ca -3 1 -1 0 + C. -1 = 0 7 -2 2 CA + czB + c3C + cD = 0 Finally, substitute c, = -4t, c, = -t, c, = 2t, and c, = t into the matrix equation. %3! %3D CA + c„B + c3C + cD = 0 ):)A + (-t)8 + (( De)c + (t)D = 0

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
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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Since the matrices are linearly dependent we must now express one of the matrices as a linear combination of the others. We first recall the given set of matrices. -1 1 3 0 0 2 D = B = 2. C = 1 -з 1 -2 Next, recall the previously created matrix equation and substitute the variables A, B, C, and D in place of the matrices. -1 1 3 0 + C, + Ca -3 1 -1 0 +C. -1 = 0 7 -2 2 CA + czB + c3C + cD = 0 Finally, substitute c, = -4t, c, = -t, c, = 2t, and c, = t into the matrix equation. %3D CA + c„B + c3C + cD = 0 De)c + (t)D = 0 )e)A + (-t)8 + ((
Transcribed Image Text:Since the matrices are linearly dependent we must now express one of the matrices as a linear combination of the others. We first recall the given set of matrices. -1 1 3 0 0 2 D = B = 2. C = 1 -з 1 -2 Next, recall the previously created matrix equation and substitute the variables A, B, C, and D in place of the matrices. -1 1 3 0 + C, + Ca -3 1 -1 0 +C. -1 = 0 7 -2 2 CA + czB + c3C + cD = 0 Finally, substitute c, = -4t, c, = -t, c, = 2t, and c, = t into the matrix equation. %3D CA + c„B + c3C + cD = 0 De)c + (t)D = 0 )e)A + (-t)8 + ((
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