() a The subspace W = {C% :): a,b, cER of M2×2 (R) is called the subspace of upper triangular с € matrices. Find a basis for W, and prove that your answer is a basis. Then, state the dimension of W.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Hello, I need help with this Linear Alegebra problem. Thank you!

{():
a
The subspace W =
: a, b, c E R} of M2x2 (R) is called the subspace of upper triangular
matrices. Find a basis for W, and prove that your answer is a basis. Then, state the dimension of W.
Transcribed Image Text:{(): a The subspace W = : a, b, c E R} of M2x2 (R) is called the subspace of upper triangular matrices. Find a basis for W, and prove that your answer is a basis. Then, state the dimension of W.
Expert Solution
Step 1

Given that the set W=ab0c  a,b,c is the subspace of M2×2.

Let B=1000, 0100,0001.

Claim 1:

B is linearly independent.

For, let α,β,γ.

α1000+β0100+γ0001=0000

That is αβ0γ=0000 α=β=γ=0. Hence B is linearly independent.

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