Matrices & Determinants
System via Adjoint — |x+y+z|
nta_pyq_2026_jan
Grade 12
Question:
If $X=\begin{bmatrix}x\\y\\z\end{bmatrix}$ is a solution of the system of equations $AX=B$, where $\text{adj}\,A=\begin{bmatrix}4&2&2\\-5&0&5\\1&-2&3\end{bmatrix}$ and $B=\begin{bmatrix}4\\0\\2\end{bmatrix}$, then $|x+y+z|$ is equal to:
Step-by-Step Solution
Key Concept: $X=A^{-1}B=\tfrac{1}{|A|}\text{adj}(A)\cdot B$. $|\text{adj}(A)|=|A|^2\Rightarrow|A|^2=100\Rightarrow|A|=\pm10$. Compute $\text{adj}(A)\cdot B$.
$|x+y+z|=2$.
Correct Answer: 1