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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.3: Matrix Algebra

Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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