Consider the matrix -5 3 4 A= 10 -8 -9 15 1 2 Show that we can write A as the product A = LU, where L, U are 3 x 3 matrices, and Lis lower triangular, while U is upper triangular. Hìnt: Row reduce A, using only row additions, to an echelon form and writing row operations as matrix multinlication

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.4: Determinants
Problem 53PS
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Consider the matrix
-5
3
4
A=
10
-8 -9
15
1
2
Show that we can write A as the product A = LU, where L, U are 3 × 3 matrices, and L is lower triangular, while
U is upper triangular. Hint: Row reduce A, using only row additions, to an echelon form and writing row operations as
matrix multiplication.
Transcribed Image Text:Consider the matrix -5 3 4 A= 10 -8 -9 15 1 2 Show that we can write A as the product A = LU, where L, U are 3 × 3 matrices, and L is lower triangular, while U is upper triangular. Hint: Row reduce A, using only row additions, to an echelon form and writing row operations as matrix multiplication.
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