Find the inverse of each of the matrices, if it exists.
\(\begin{bmatrix} 3 & 10\\ 2 & 7\end{bmatrix}\)
\(\begin{bmatrix} 3 & 10\\ 2 & 7\end{bmatrix}\)
Solution and Explanation
Let A=\(\begin{bmatrix} 3 & 10\\ 2 & 7\end{bmatrix}\)
We know that \(A = IA \)
\(\begin{bmatrix} 3 & 10\\ 2 & 7\end{bmatrix}\)= \(\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix}\)A
⇒ \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)= \(\begin{bmatrix} 1 & -1\\ 0 & 1\end{bmatrix}\)A \((R_1\rightarrow R_1-R_2)\)
⇒ \(\begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix}\)= \(\begin{bmatrix} 1 & -1\\ -2 & 3\end{bmatrix}\) A \((R_2\rightarrow R_2-2R_2)\)
⇒ \(\begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix}\)= \(\begin{bmatrix} 7 & -10\\ -2 & 3\end{bmatrix}\)\(A\)et \((R_1\rightarrow R_1-3R_2)\)
\(\therefore A^{-1}=\) \(\begin{bmatrix} 7 & -10\\ -2 & 3\end{bmatrix}\)
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix} \). The determinant of \( A^3 \) is:
- Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.
- The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :
- If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
- If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :
Questions Asked in CBSE CLASS XII exam
- Radhika, Mehar, and Shubha were partners in a firm sharing profits and losses in the ratio of 9:8:7. If Radhika's share of profit at the end of the year amounted to Rs 5,40,000, Shubha's share of profit will be:
- CBSE CLASS XII - 2025
- Partnership Accounts
- Cite two evidences from the text to show that gender bias is still a hindrance in the progress of women in society.
- CBSE CLASS XII - 2025
- Reading Comprehension
- What is so ironical about Sam reaching the third level?
- CBSE CLASS XII - 2025
- Literature
- Which of the following is not a greenhouse gas?
- CBSE CLASS XII - 2025
- Environment Awareness
- Name the various advanced technologies adopted in emission control.
- CBSE CLASS XII - 2025
- Automotive Systems and Maintenance
Concepts Used:
Invertible matrices
A matrix for which matrix inversion operation exists, given that it satisfies the requisite conditions is known as an invertible matrix. Any given square matrix A of order n × n is called invertible if and only if there exists, another n × n square matrix B such that, AB = BA = In, where In is an identity matrix of order n × n.
For example,
It can be observed that the determinant of the following matrices is non-zero.
