Consider the following matrix A = R1 + 7R2 R3 -2R2 or -40 13 R4-3/2R2 9 -5 -3 16 (1) Find the inverse matrix A-¹ by row reducing [A | I3]. Instructions for row reducing: Label each step of row reducing by the elementary row operations used with notation or a 5 -2 -1 a Ri Ri Rj Ri+aRj (which happen to be of type I or II or III, but do not put that in your label) as appropriate, with the rows i or j involved and constants a involved. It is ok if one step combines several type III moves (or several type II or several type I) in which case stack your labels like 9R3 1/5R1 or using what you learned in part (1). Show your work. but you may not combine more moves than that. It is also ok to write the longer R1 R1 + 7R2 or R39R3 as your labels. (If instructios are not clear, please go to office hours for clarification. There are office hours daily. See Piazza.) You do not need to show your scratch work arithmetic. (2) Solve the following system of equations -40x1 + 16x2 +9x3 = 0 13x15x2 3x3 = 0 5x₁2x₂x3 = 2 R1 R2 R1 + R2

Consider the following matrix A = R1 + 7R2 R3 -2R2 or -40 13 R4-3/2R2 9 -5 -3 16 (1) Find the inverse matrix A-¹ by row reducing [A | I3]. Instructions for row reducing: Label each step of row reducing by the elementary row operations used with notation or a 5 -2 -1 a Ri Ri Rj Ri+aRj (which happen to be of type I or II or III, but do not put that in your label) as appropriate, with the rows i or j involved and constants a involved. It is ok if one step combines several type III moves (or several type II or several type I) in which case stack your labels like 9R3 1/5R1 or using what you learned in part (1). Show your work. but you may not combine more moves than that. It is also ok to write the longer R1 R1 + 7R2 or R39R3 as your labels. (If instructios are not clear, please go to office hours for clarification. There are office hours daily. See Piazza.) You do not need to show your scratch work arithmetic. (2) Solve the following system of equations -40x1 + 16x2 +9x3 = 0 13x15x2 3x3 = 0 5x₁2x₂x3 = 2 R1 R2 R1 + R2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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