Digital ACT Math Practice Question #1162
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Recall that a 2x2 matrix has no inverse when det(A) = ad - bc = 0. Set up the quadratic equation and factor.
Desmos Shortcut: In Desmos, type y = 2x^2 - 2x - 12. The x-intercepts are clearly at x = -2 and x = 3.
A matrix has no inverse if and only if its determinant is zero: det(A) = (2k)(k - 1) - (4)(3) = 0 => 2k^2 - 2k - 12 = 0. Divide by 2: k^2 - k - 6 = 0 => (k - 3)(k + 2) = 0 => k = 3 or k = -2. Thus Option A is the correct answer....
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
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