Matrices & Determinants
Infinite Solutions — Computing Combined Expression
nta_pyq_2023_apr
Grade 12
Question:
If the system $2x+y-z=5$, $2x-5y+\lambda z=\mu$, $x+2y-5z=7$ has infinitely many solutions, then $(\lambda+\mu)^2+(\lambda-\mu)^2$ is equal to
Step-by-Step Solution
Key Concept: For infinite solutions: $\Delta=0$ gives $\lambda=17$; $\Delta_3=0$ (or another minor) gives $\mu=-13$.
$\lambda=17,\ \mu=-13$. $(\lambda+\mu)^2+(\lambda-\mu)^2=900+16=916$.
Correct Answer: 2