Q147 / 240 · KCET 2026 · Mathematics
Match List-I with List-II
List-I List-II a) A matrix which is not a square matrix i) Symmetric matrix b) A square matrix $A = A'$ ii) Null matrix c) The diagonal elements of a diagonal matrix are same iii) Rectangular matrix d) A matrix which is both symmetric and skew symmetric iv) Scalar matrix
| List-I | List-II | ||
|---|---|---|---|
| a) | A matrix which is not a square matrix | i) | Symmetric matrix |
| b) | A square matrix $A = A'$ | ii) | Null matrix |
| c) | The diagonal elements of a diagonal matrix are same | iii) | Rectangular matrix |
| d) | A matrix which is both symmetric and skew symmetric | iv) | Scalar matrix |
- Aa - iii, b - i, c - ii, d – iv
- Ba - iii, b - ii, c - iv, d – i
- Correct answerCa - iii, b - i, c - iv, d – ii
- Da - iii, b - iv, c - i, d – ii
Solution
a) A matrix which is not a square matrix has an unequal number of rows and columns, which is known as a rectangular matrix. (a $\rightarrow$ iii)
b) A square matrix satisfying $A = A'$ is defined as a symmetric matrix. (b $\rightarrow$ i)
c) A diagonal matrix in which all the principal diagonal elements are equal is called a scalar matrix. (c $\rightarrow$ iv)
d) If a matrix is both symmetric and skew-symmetric, then $A = A'$ and $A = -A'$. This implies $A = -A$, which gives $2A = 0$, so $A$ is a null matrix. (d $\rightarrow$ ii)
The correct matching is a - iii, b - i, c - iv, d - ii.
Answer: a - iii, b - i, c - iv, d – ii
b) A square matrix satisfying $A = A'$ is defined as a symmetric matrix. (b $\rightarrow$ i)
c) A diagonal matrix in which all the principal diagonal elements are equal is called a scalar matrix. (c $\rightarrow$ iv)
d) If a matrix is both symmetric and skew-symmetric, then $A = A'$ and $A = -A'$. This implies $A = -A$, which gives $2A = 0$, so $A$ is a null matrix. (d $\rightarrow$ ii)
The correct matching is a - iii, b - i, c - iv, d - ii.
Answer: a - iii, b - i, c - iv, d – ii
Hence, the correct answer is option: 'C'.