Matrices & Determinants
System of Equations
MMTS_Full_Test_10
Grade 12
Question:
The number of distinct real values of $K$ such that the system of equations $x+2y+z=1$, $x+3y+4z=K$, $x+5y+10z=K^2$ has infinitely many solutions is
Step-by-Step Solution
Key Concept: For infinite solutions, $\Delta=0$ and $\Delta_1=\Delta_2=\Delta_3=0$
$\Delta=0$ always (check). For infinite solutions: $K^2-3K+2=0\Rightarrow K=1$ or $K=2$. So 2 values.
Correct Answer: 3