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Question Find the following given the matrices. 14 55 21 where z and are unknown values. a) Evaluate 5A - 4B; -3 2-15 -1 z -4-10 and 4-3 19 -1 b) Find the matrix Y that satisfies the matrix equation I-7Y = 4C - 12Y. Give your answer in exact (fractional) form. c) Use matrix multiplication to find AB. Show your working. d) Use matrix multiplication to find BA. Show your working.

Question Find the following given the matrices. 14 55 21 where z and are unknown values. a) Evaluate 5A - 4B; -3 2-15 -1 z -4-10 and 4-3 19 -1 b) Find the matrix Y that satisfies the matrix equation I-7Y = 4C - 12Y. Give your answer in exact (fractional) form. c) Use matrix multiplication to find AB. Show your working. d) Use matrix multiplication to find BA. Show your working.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question Find the following given the matrices. A = -8-4 1 5 5 14 B = 5 3 where and are unknown values. 2 1 1 2 -15 8 -3 -1 I -4-10 4-3 19 -7 and C= 8 4 -1 0 5 2 1 a) Evaluate 5A - 4B; b) Find the matrix Y that satisfies the matrix equation I-7Y = 4C - 12Y. Give your answer in exact (fractional) form. c) Use matrix multiplication to find AB. Show your working. d) Use matrix multiplication to find BA. Show your working. e) What values of x (if any) will make the matrix product BA, found in part (d), equal to an identity matrix? Check your result by substitution (if there is solution). f) Find det C in terms of z by expanding along any column. For what value of z will the matrix C be singular? Show your working.
Transcribed Image Text:Question Find the following given the matrices. A = -8-4 1 5 5 14 B = 5 3 where and are unknown values. 2 1 1 2 -15 8 -3 -1 I -4-10 4-3 19 -7 and C= 8 4 -1 0 5 2 1 a) Evaluate 5A - 4B; b) Find the matrix Y that satisfies the matrix equation I-7Y = 4C - 12Y. Give your answer in exact (fractional) form. c) Use matrix multiplication to find AB. Show your working. d) Use matrix multiplication to find BA. Show your working. e) What values of x (if any) will make the matrix product BA, found in part (d), equal to an identity matrix? Check your result by substitution (if there is solution). f) Find det C in terms of z by expanding along any column. For what value of z will the matrix C be singular? Show your working.
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