Find the transpose of each of the following matrices:
I.\(\begin{bmatrix}5\\\frac{1}{2}\\-1\end {bmatrix}\)
II.\(\begin{bmatrix}1&-1\\2&3\end{bmatrix}\)
III.\(\begin{bmatrix}-1&5&6\\\sqrt3&5&6\\2&3&-1\end{bmatrix}\)
Find the transpose of each of the following matrices:
I.\(\begin{bmatrix}5\\\frac{1}{2}\\-1\end {bmatrix}\)
II.\(\begin{bmatrix}1&-1\\2&3\end{bmatrix}\)
III.\(\begin{bmatrix}-1&5&6\\\sqrt3&5&6\\2&3&-1\end{bmatrix}\)
Solution and Explanation
(i) Let A=\(\begin{bmatrix}5\\\frac{1}{2}\\-1\end {bmatrix}\)
then A-T= \(\begin{bmatrix}5&\frac{1}{2}&-1\end{bmatrix}\)
(ii)Let A= \(\begin{bmatrix}1&-1\\2&3\end{bmatrix}\)
then A-T= \(\begin{bmatrix}1&2\\-1&3\end{bmatrix}\)
(iii)Let A= \(\begin{bmatrix}-1&5&6\\\sqrt3&5&6\\2&3&-1\end{bmatrix}\)
then A-T = \(\begin{bmatrix}-1&\sqrt3&2\\5&5&3\\6&6&-1\end{bmatrix}\)
Top Questions on Matrices
Let
\( A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{bmatrix} \)
and \(|2A|^3 = 2^{21}\) where \(\alpha, \beta \in \mathbb{Z}\). Then a value of \(\alpha\) is:
- If \(A = \begin{bmatrix} 3 & 2 \\ -1 & 1 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} -1 & 0 \\ 2 & 5 \\ 3 & 4 \end{bmatrix},\)then \((BA)^T\) is equal to:
- If \( A = \begin{bmatrix} K & 4 \\ 4 & K \end{bmatrix} \) and \( |A^3| = 729 \), then the value of \( K^8 \) is:
- Let $A$ be a matrix such that $A^2 = I$, where $I$ is an identity matrix. Then $(I + A)^4 - 8A$ is equal to:
- Let $A = I_2 - MM^T$, where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M = I_1$ holds. If $\lambda$ is a real number such that the relation $AX = \lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:
Questions Asked in CBSE CLASS XII exam
What is the Planning Process?
- CBSE CLASS XII - 2023
- Planning process steps
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)
- CBSE CLASS XII - 2021
- Determinants
- Find the vector and the cartesian equations of the lines that pass through the origin and(5,-2,3).
- CBSE CLASS XII - 2021
- Three Dimensional Geometry
- How much charge is required for the following reductions:
(i) 1 mol of Al3+ to Al.
(ii) 1 mol of Cu2+ to Cu.
(iii) 1 mol of MnO-4 to Mn2+ .- CBSE CLASS XII
- Electrochemistry
- Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the to charges is the electric potential zero? Take the potential at infinity to be zero.
- CBSE CLASS XII
- electrostatic potential and capacitance
Concepts Used:
Transpose of a Matrix
The matrix acquired by interchanging the rows and columns of the parent matrix is called the Transpose matrix. The transpose matrix is also defined as - “A Matrix which is formed by transposing all the rows of a given matrix into columns and vice-versa.”
The transpose matrix of A is represented by A’. It can be better understood by the given example:
Now, in Matrix A, the number of rows was 4 and the number of columns was 3 but, on taking the transpose of A we acquired A’ having 3 rows and 4 columns. Consequently, the vertical Matrix gets converted into Horizontal Matrix.
Hence, we can say if the matrix before transposing was a vertical matrix, it will be transposed to a horizontal matrix and vice-versa.
Read More: Transpose of a Matrix