Let A be a 80 x 90 matrix (80 rows and 90 columns). Does the homogeneous 0 always has nonzero solutions. (Hint: You may use the Rank Theorem to show 3. equation Ax that the subspace NulA is always nonzero.)

Q: Determine if the vector u is in the column space of matrix A and whether it is in the null space of…

A: 1.A vector v is in the column space of a matrix A if AX=v has a solution(X satisfying the equation…

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A: solution of the given problem is below ...

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Q: What can be said about Nul A if A is a 5×7 ​matrix? Could it be the zero​ subspace? Why or why​ not?

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A: See the detailed solution below.

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Q: 3. Suppose W (a) (b) a = = {( 2 ): 9₂ Prove that W is a subspace of M2x2 (R). : a, b, c ER CER}.…

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