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1 2 0 Next, let A 4 4 1 We can use Gauss elimination with two 0 8 2 steps (and no row exchanges) to put A in upper triangular form. This elimination can also be viewed as factoring the matrix: A = LU, where L is lower triangular and A is upper triangular. In this case, L || and U We can also use this factorization to solve a system of equations. 1 Say we want to solve Ax = 3 First, use forward substitution 14 1 to solve Ly 3 obtaining y = 14 After that, we can solve Ux = y to get x = -1 00

1 2 0 Next, let A 4 4 1 We can use Gauss elimination with two 0 8 2 steps (and no row exchanges) to put A in upper triangular form. This elimination can also be viewed as factoring the matrix: A = LU, where L is lower triangular and A is upper triangular. In this case, L || and U We can also use this factorization to solve a system of equations. 1 Say we want to solve Ax = 3 First, use forward substitution 14 1 to solve Ly 3 obtaining y = 14 After that, we can solve Ux = y to get x = -1 00

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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1 2 0 Next, let A = 4 4 1 We can use Gauss elimination with two 0 8 2 steps (and no row exchanges) to put A in upper triangular form. This elimination can also be viewed as factoring the matrix: A = LU, where L is lower triangular and A is upper triangular. In this case, L and U We can also use this factorization to solve a system of equations. Say we want to solve Ax 3 First, use forward substitution 14 1 to solve Ly 3 , obtaining y = 14 After that, we can solve Ux y to get x = 1 1 3
Transcribed Image Text:1 2 0 Next, let A = 4 4 1 We can use Gauss elimination with two 0 8 2 steps (and no row exchanges) to put A in upper triangular form. This elimination can also be viewed as factoring the matrix: A = LU, where L is lower triangular and A is upper triangular. In this case, L and U We can also use this factorization to solve a system of equations. Say we want to solve Ax 3 First, use forward substitution 14 1 to solve Ly 3 , obtaining y = 14 After that, we can solve Ux y to get x = 1 1 3
What is the 3x3 permutation matrix P that puts row 1 into row 2, puts row 2 into row 3, and puts row 3 into row 1? P
Transcribed Image Text:What is the 3x3 permutation matrix P that puts row 1 into row 2, puts row 2 into row 3, and puts row 3 into row 1? P
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