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
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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![Consider the following matrix
A
(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
R1 + 7R2
R3 -2R2 or
-40
16
9
13 -5 -3
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
R4-3/2R2
9R3
1/5R1 or
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
13x15x2 3x3 = 0
= 2
5x12x2x3
=
0
R1 + R2
R1 + R2
using what you learned in part (1). Show your work.
Optional on scratch paper (that you will not hand in) verify your answers. For (1) you can do this by
multiplying out AA-¹ or A-¹A. For (2) you can do this by plugging back in your solution (unless you found
that there was no solution).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c07aab6-53ae-4bda-bd88-033e72af521a%2F3c61431c-fe10-4f19-8d5f-7215e46e8a56%2F1qcji7_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following matrix
A
(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
R1 + 7R2
R3 -2R2 or
-40
16
9
13 -5 -3
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
R4-3/2R2
9R3
1/5R1 or
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
13x15x2 3x3 = 0
= 2
5x12x2x3
=
0
R1 + R2
R1 + R2
using what you learned in part (1). Show your work.
Optional on scratch paper (that you will not hand in) verify your answers. For (1) you can do this by
multiplying out AA-¹ or A-¹A. For (2) you can do this by plugging back in your solution (unless you found
that there was no solution).
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