Matrices
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See all →- If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) satisfies \(A^2-5A-2I=O\), then \(A^{-1}\) equals Answer: A. 1/2(A-5I) A(A-5I)=2I⇒ A⁻¹=1/2(A-5I) . 1
- If \(A\) is a square matrix of order 3 with \(|A|=4\), then \(|\operatorname{adj}(2A)|\) is Answer: B. 1024 |2A|=2³·4=32 ; |adjB|=|B|² for order 3, so 32²=1024 . 1
- The system \(x+y+z=1,\ x+2y+3z=2,\ x+3y+kz=3\) has infinitely many solutions when \(k=\) Answer: B. 5 Δ=k-5=0⇒ k=5 . Then E₂-E₁ and E₃-E₂ both give y+2z=1 , so the system is consistent. 1