Suppose A is a square matrix. For the following questions, give a rigorous explanation or counterexample. (a) Is im(A) necessarily equal to im(rref(A))? (b) Suppose A is invertible. Is im(A) = im(rref(A)) ? (c) Suppose im(A) = im(rref(A)). Is A invertible?

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Q: (c) Consider the quadratic form f(x1, x2, x3) = 3(a₁x₁ + a2x2 + a3x3)² = 4(b₁x₁ + b₂x2 + b3x3)². (i)…

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