Find the dimension of the subspace W =

Nesma

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2022-05-28

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Find the dimension of the subspace

of M2,2.

Physics, textbook solutions, Physics textbook-solutions,

Nesma

2022-05-28

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The equations specified are equivalent to the system

a + b − c = 0

b + c − d = 0

a − c − d = 0

The coefficient matrix of this system row-reduces to

Thus, every solution can be decribed with a suitable choice of d, together with a = 3d, b = -d and c = 2d. Thus the subspace W can be described as

So, W is a subspace of M₂_,₂ with dimension 1.

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