Is it true that the set of all 4 x 4 matrices with a trace of 0 is a subspace of Max4? If so, prove it. If not, provide a counterexample to show you are correct. Is it true that the set of all 4x 4 matrices with identical entries on the diag- onal a subspace of Max4? If so, prove it. If not, provide a counterexample to show you are correct.

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A: See the solution below.

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Q: elementary

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A: The objective is to find true or false of the above statements.

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A: Prove that a matrix with a column of zeros cannot have an inverse.

Q: When two m x n matrices are said to be equal? Explain there Applicability?

A: Two mxn matrices are said to be equal if their corresponding elements are equal.

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Q: = 0 = 0 - = 0 2. 2y" - Зу' %3D 0 4. 2y" - 7у' + Зу %3D 0 6. у" + 5y' + 5у %3D 0 8. у" — бу' + 13у…

A: Given differential equation has constant cofficient so We can solve by auxillary equation.

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