Robert Z. answered • 11/19/20

3965+ hours (& counting!) tutoring math -- Prealgebra to Calculus 2

Hi Sana,

A good hunch would be "d." The first choice doesn't seem reasonable: multiplying a generic 3x1 vector by A will produce non-zero results in every element.

For the second choice, the transpose A^{T} is:

1 a b

0 1 a ≠ A

0 0 0

How the determinant could be negative for ALL values of a and b (as answer c states) is hard to imagine, so by POE, answer d makes sense, but we'll calculate it to be sure.

However, det A = 1-a

This is not equivalent to a^{2}- b, and it is not always <0, so the answer is "none of the above."