Question:
Compute \([\,6\ \ 5\,]\begin{bmatrix}1 \\ -1\end{bmatrix}=\) ?
Compute \([\,6\ \ 5\,]\begin{bmatrix}1 \\ -1\end{bmatrix}=\) ?
Show Hint
Always check sizes: \((1\times2)\cdot(2\times1)\to(1\times1)\).
Updated On: Oct 17, 2025
- \([\,6\ \ -5\,]\)
- \([\, -5\ \ 6\,]\)
- \([\,1\,]\)
- \([\,1\ \ 1\,]\)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Idea. Row–column multiplication: multiply matching entries and add. A \(1\times2\) times \(2\times1\) gives a \(1\times1\) number.
\[ 6\cdot 1+5\cdot(-1)=6-5=1. \]
\[ 6\cdot 1+5\cdot(-1)=6-5=1. \]
Was this answer helpful?
0
0
Top Questions on Matrix Operations
- Let $ A = [a_{ij}] $ be a $3 \times 3 $ matrix such that: $$ A = \begin{bmatrix} 0 & 0 & 4 \\ 1 & 0 & 0 \\ 0 & 1 & 3 \\ \end{bmatrix}, A^{-1} = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 3 & 0 \\ 2 & 1 & 0 \end{bmatrix}. $$ Then $ a_{23} $ equals:
- JEE Main - 2025
- Mathematics
- Matrix Operations
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
- JEE Main - 2025
- Mathematics
- Matrix Operations
- Match List-I with List-II.\[\begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}, \; \Delta \text{ is} & (I) \; 0 \\ \hline (B) \; \text{If } A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}, \; \Delta \text{ is} & (II) \; 1 \\ \hline (C) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}, \; |A^{-1}| \text{ is} & (III) \; -2 \\ \hline (D) \; \text{If } A = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}, \; a \text{ is} & (IV) \; 2 \\ \hline \end{array}\]
- CUET (PG) - 2025
- Computer Science
- Matrix Operations
- If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).
- KEAM - 2025
- Mathematics
- Matrix Operations
- Multiply the matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \]
- Bihar Board XII - 2025
- Mathematics
- Matrix Operations
View More Questions
Questions Asked in Bihar Board XII exam
- Explain the characteristics of a good brand.
- Bihar Board XII - 2025
- Entrepreneurship: Concept, Functions and Need
- Explain the different kinds of capital.
- Bihar Board XII - 2025
- Business Strategy
- What are the responsibilities of an entrepreneur towards society? Explain.
- Bihar Board XII - 2025
- Entrepreneurship: Concept, Functions and Need
- Define planning and mention its features.
- State any two objectives of project report.
- Bihar Board XII - 2025
- Project Planning
View More Questions