Digital ACT Math Practice Question #852
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Recall the 2x2 determinant formula: \( \det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc \). Be extremely careful with negative signs when subtracting \( bc \).
Tactical Shortcut: Calculate \( \det(B) \) first. Once you have \( \det(B) = 20 \), double it to 40. Then write \( 4k - (-6) = 40 \) and solve for \( k \).
Step 1: Calculate the determinant of matrix \( B \): \[ \det(B) = (6)(3) - (1)(-2) = 18 + 2 = 20 \] Step 2: State the condition: \( \det(A) = 2 \cdot \det(B) = 2(20) = 40 \). Step 3: Calculate \( \det(A) \) in terms of \( k \): \[ \det(A) =...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
Unlock Full Solution & 2,600+ Official Drills
Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.
Matrix \( A \) is defined as \( \begin{pmatrix} 2k & 4 \\ 3 & k-1 \end{pmatrix} \). For which of the following values of...
If $\log_{10}(x) = 2$ and $\log_{10}(y) = -3$, what is the value of $\log_{10}\left(\frac{100x^3}{\sqrt{y}}\right)$?...
A 20-foot ladder leans against a vertical wall, making an angle of 70° with the level ground. Which of the following exp...
What is the resulting matrix product of [[3, 1], [2, -1]] * [[2], [5]]?...