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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
MCQ
Consider the matrices $A=\begin{bmatrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5\end{bmatrix}, B=\begin{bmatrix} 2 & 4 \\ 0 & 1 \\ -1 & 2\end{bmatrix}, C=\begin{bmatrix} 3 \\ 1 \\ 2\end{bmatrix}$. Out of the givenmatrix products, ___________
$(\mathrm{AB})^{\top} \mathrm{C}$
$\mathrm{C}^{\top} \mathrm{C}(A B)^{\top}$
$C^{\top} A B$
$\mathrm{A}^{\top} \mathrm{ABB}^{\top} \mathrm{C}$
  • A
    Exactly one is defined
  • B
    Exactly two are defined
  • ✓
    Exactly three are defined
  • D
    all four are defined
✓

Answer

Correct option: C.
Exactly three are defined
Exactly three are defined
A is of order 3 × 3, B is of order 3 × 2 and C is of order 3 × 1.
$(A B)^{\top} C$ is of order $2 \times 1$
$C^{\top} C$ and $(A B)^{\top}$ are of different orders.
$C^{\top} C(A B)^{\top}$ is not defined.
$C^{\top} A B$ is of order $1 \times 2$.
$\mathrm{A}^{\top} \mathrm{ABB}^{\top} \mathrm{C}$ is of order $3 \times 1$.

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