Matrices & Determinants
Linear system — solution conditions
MJAT_TS5_P2
Grade 12
Question:
**Paragraph (continued):** Consider the system $x+2y-3z=a$; $2x+6y-11z=b$; $x-2y+7z=c$. Then the system:
A) has a unique solution when $5a=2b+c$
B) has infinite number of solutions when $5a=2b+c$
C) has no solution for all $a,b,c$
D) has a unique solution for all $a,b,c$
A) has unique solution when $5a=2b+c$
B) has infinite solutions when $5a=2b+c$
C) has no solution for all $a,b,c$
D) has unique solution for all $a,b,c$
Step-by-Step Solution
Key Concept: Check $\det(A)$: from the coefficient matrix. If $\det=0$, the system may have infinite or no solutions depending on the RHS. The condition $5a=2b+c$ ensures consistency for infinite solutions.
Answer: **B**.
Correct Answer: B