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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 = Part III 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 =

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 = Part III 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 =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 6E
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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 = Part III 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: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 = Part III 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 =
Part I 2 1 Let A We can make A into an upper triangular matrix 6 5 using just one elimination step, and that step can be represented by an elimination matrix, E, so that EA = U is upper triangular. In this case, E = and U = E-lU, or, if we Also, we can rearrange the equation to get A E-',we can say A = write L LU, where L = Part II 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
Transcribed Image Text:Part I 2 1 Let A We can make A into an upper triangular matrix 6 5 using just one elimination step, and that step can be represented by an elimination matrix, E, so that EA = U is upper triangular. In this case, E = and U = E-lU, or, if we Also, we can rearrange the equation to get A E-',we can say A = write L LU, where L = Part II 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
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