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)

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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Question

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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2x+y+z=7 4x−3y+2z=4 3x+2y−2z=5 Write the system in matrix form Ax=B. Determine the inverse matrix A−1. Use the inverse matrix to find the solution vector x.
This question has several parts that must be completed sequentially. If you skip a part of the question, you will no Tutorial Exercise Find x and y. X + 2 3. -8 2x + 5 3 -8 4 2y 2x 4 16 -6 8-9 y+ 2 8-9 10 Step 1 Recall that if two matrices are equal then their corresponding entries are equal. Using this fact, write an equation using entries corresponding to a1 and solve it. Remember is the entry in the /th row and th column. X + 2 = Subm Skip (you cannot come back) Need Help? Read it