forms a subspace of all

What is the dimension of W? Find a basis for W.

Dottie Parra
2021-01-25
Answered

Show that W, the set of all $3\times 3$ upper triangular matrices,

forms a subspace of all$3\times 3$ matrices.

What is the dimension of W? Find a basis for W.

forms a subspace of all

What is the dimension of W? Find a basis for W.

You can still ask an expert for help

StrycharzT

Answered 2021-01-26
Author has **102** answers

To show that W, the set of all

forms asubspace of all

Now we know that M, the set of all

Let A, B in W with

and k be a scalar. Now,

Once again,

Therefore, W is a subspace of M. Now let x is a typical element of W, with

can be written as

where

Now for any linear combination

imply

Therefore,

hence dim

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