Consider the following subspace of R. a +b+6c a +b+ 6c+2d -2 a + 26 - 8 c + 2d b+c+5d W = : a, b, c, d eR 1) Show that W is the column space of A for some matrix A to be determined. 2) Determine a basis for W. What is the dimension of W? 3) Determine a basis for Null(A). 4) State the rank-nullity theorem. Verify it for this matrix A.

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