Matrices & Determinants
Determinant of Adjoint Power of Scaled Matrix
nta_pyq_2023_apr
Grade 12
Question:
Let $\det(A)=m-n$ where $4m+n=22$ and $17m+4n=93$. If $\det(n\,\text{adj}(\text{adj}(mA)))=3^a5^b6^c$, then $a+b+c$ is equal to
Step-by-Step Solution
Key Concept: Solve: $m=5,\ n=2$. Order of $A$ is $m=5$. $|A|=m-n=3$. Compute $\det(2\,\text{adj}(\text{adj}(5A)))$.
$a=11,\ b=80,\ c=5$. $a+b+c=96$.
Correct Answer: 2