a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2...

a. Prove that y=sin(x) is a subspace of R^2

b. Prove that a set of 2x2 non invertible matrices a subspace of all 2x2 matrices

Solutions

Expert Solution

b. A 2 2 is said to be non invertible if and only if determinant is zero .

Let S = set of all 2 2 non - invertible matrix .

Suppose A ,B S

det (A) = 0 and Det (B) = 0

Now det(AB) = det(A) . det(B) =0 .0 =0

AB S

Also det (cA) = c² det (A) = c² . 0 = 0

cA S

So A , B S then AB S and cA S

Hence S i.e., set of all 2 2 non invertible matrix forms a subspace set of all 2 2 matrices .

a. y = sin (x) is not forms a subspace of .

Because every proper suspace of is a straight line through origin but sin(x) is not .

If you have any doubt or need more clariication at any step please comment .

Colby Messinger answered 1 year ago

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Question

a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2...

Solutions

Expert Solution

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