Home › JEE Main › Mathematics › Matrices and Determinants › System of equations Ax = b has unique solution i…
System of equations Ax = b has unique solution iff:
AMore equations than unknowns
Bb = 0
C|A| ≠ 0 (A is non-singular, equivalently invertible)
D|A| = 0
Answer & Solution
Correct answer: C. |A| ≠ 0 (A is non-singular, equivalently invertible)
For square A: unique solution iff |A| ≠ 0 (then x = A⁻¹ b). If |A| = 0: either no solution (inconsistent) or infinitely many (under-determined).
Related questions
Three points $(1, 2), (3, 4), (5, 6)$ on the school graph paper are:If $A$ is a $3\times 3$ matrix with $|A| = 5$, then $|A^{-1}|$ is:Swapping two rows of a determinant changes its value by a factor of:The determinant of $\begin{pmatrix}3 & 2 \\ 1 & 4\end{pmatrix}$ is:A square matrix $A$ has an inverse if and only if:A square matrix $A$ is symmetric if:The transpose of $A^T$ is:The product of a matrix $A$ of order $2\times 3$ and $B$ of order $3\times 4$ has order: