L3x3 + M (subspace sum). sym 3×3 !! L3x3 O M (direct sum). sym 3×3 !! express A E M3x3 as A = L+U where L is lower triangular and U is upper Then add and subtract UT. Explain your answers for both statements.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
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4. Which of the following statements are true?
(a) M3x3 = L3x3 + M (subspace sum).
sym
3×3
(b) M3x3 = L3x3 O M (direct sum).
Hint: first express A E M3×3 as A = L+U where L is lower triangular and U is upper
triangular. Then add and subtract U". Explain your answers for both statements.
Transcribed Image Text:4. Which of the following statements are true? (a) M3x3 = L3x3 + M (subspace sum). sym 3×3 (b) M3x3 = L3x3 O M (direct sum). Hint: first express A E M3×3 as A = L+U where L is lower triangular and U is upper triangular. Then add and subtract U". Explain your answers for both statements.
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