NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.5 Question 5

Question

Examine consistency. Use the matrix method for AX=B, where A = $\left[\begin{matrix}3 & -1 & -2\0 & 2 & -1\3 & -5 & 0\end{matrix}\right]$, B = $\left[\begin{matrix}2\-1\3\end{matrix}\right]$, X=$\left[\begin{matrix}x\y\z\end{matrix}\right]$.

Accepted Answer

Final Answer: Inconsistent; no solution. Step 1: Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ. Step 2: The cofactors in this row are $\left[\begin{matrix}-5 & -3 & -6\end{matrix}\right]$. Step 3: The expansion terms are $-15$, $3$, $12$. Step 4: Adding and simplifying gives det A = $0$. Step 5: First check whether this determinant is zero. Step 6: The determinant vanishes, so the matrix is singular and has no inverse. Step 7: The coefficient rank is 2 and the augmented rank is 3. Step 8: Unequal ranks establish inconsistency.

NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.5 Question 5

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