In the matrix A= \(\begin{bmatrix} 2 & 5 & 19&-7 \\ 35 & -2 & \frac{5}{2}&12 \\ \sqrt3 & 1 & -5&17 \end{bmatrix}\),write:
I. The order of the matrix
II. The number of elements
III. Write the elements a13, a21, a33, a24, a23
In the matrix A= \(\begin{bmatrix} 2 & 5 & 19&-7 \\ 35 & -2 & \frac{5}{2}&12 \\ \sqrt3 & 1 & -5&17 \end{bmatrix}\),write:
I. The order of the matrix
II. The number of elements
III. Write the elements a13, a21, a33, a24, a23
Solution and Explanation
(i) In the given matrix, the number of rows is 3 and the number of columns is 4.
Therefore, the order of the matrix is 3 × 4.
(ii) Since the order of the matrix is 3 × 4, there are 3 × 4 = 12 elements in it.
(iii) \(a_{13}=19, a_{21}=35,a_{33}=-5,a_{24}=12,a_{23}=\frac{5}{2}\)
Top Questions on Matrices
- If A is a square matrix of order 4 and |A| = 4, then |2A| will be:
- If \( A \) is a square matrix and \( I \) is an identity matrix such that \( A^2 = A \), then \( A(I - 2A)^3 + 2A^3 \) is equal to:
- If \([A]_{3 \times 2} [B]_{x \times y} = [C]_{3 \times 1}\), then \( x \) and \( y \) are:
- Solve the system of equations by matrix method: \[ 2x + 3y + 3z = 5 \] \[ x - 2y + z = -4 \] \[ 3x - y - 2z = 3 \]
If matrix \[ A = \begin{bmatrix} 1 & 1 & 3 \\ 1 & 3 & -3 \\ -2 & -4 & -4 \end{bmatrix}, \] then find \( A^{-1} \).
Questions Asked in CBSE CLASS XII exam
(a) State the following:
(i) Kohlrausch law of independent migration of ions
- CBSE CLASS XII - 2025
- Electrolytic Cells and Electrolysis
A solution of glucose (molar mass = 180 g mol\(^{-1}\)) in water has a boiling point of 100.20°C. Calculate the freezing point of the same solution. Molal constants for water \(K_f\) and \(K_b\) are 1.86 K kg mol\(^{-1}\) and 0.512 K kg mol\(^{-1}\) respectively.
- CBSE CLASS XII - 2025
- Colligative Properties
Write the reactions involved when D-glucose is treated with the following reagents: (a) HCN (b) Br\(_2\) water
- CBSE CLASS XII - 2025
- Oxidation And Reduction Reactions
Identify A and B in each of the following reaction sequence:
(a) \[ CH_3CH_2Cl \xrightarrow{NaCN} A \xrightarrow{H_2/Ni} B \](b) \[ C_6H_5NH_2 \xrightarrow{NaNO_2/HCl} A \xrightarrow{C_6H_5NH_2} B \]
- CBSE CLASS XII - 2025
- Organic Reactions
Would you expect benzaldehyde to be more reactive or less reactive in nucleophilic addition reactions than propanal? Justify your answer.
- CBSE CLASS XII - 2025
- Aldehydes And Ketones
Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.