In the third-order matrix, a_(ij) denotes the element of the i^(th) row and j^(th) column: a_(ij) = {0, i ≠ j; 1, i = j} Statement I: A Matrix is an upper…

Answer: (c) Both I and II. The matrix with a_(ij) = 1 for i = j and 0 otherwise is the identity matrix I₃. All entries below the diagonal are 0, so it is upper triangular (Statement I is true), and |I₃| = 1 (Statement II is true). Correct: (c)

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Mathematics20251 markMCQMatrices

Choose the correct option.

In the third-order matrix, a_(ij) denotes the element of the i^(th) row and j^(th) column: a_(ij) =…

In the third-order matrix, $a_{ij}$ denotes the element of the $i^{\text{th}}$ row and $j^{\text{th}}$ column: $a_{ij} = \begin{cases} 0, & i \neq j \\ 1, & i = j \end{cases}$ Statement I: A Matrix is an upper triangular matrix. Statement II: The determinant of the matrix is equal to 1. Which of the above statement/s is/are correct?

(a)Only I.
(b)Only II.
(c)Both I and II.
(d)Neither I nor II.

Answer

Correct option: (c)

Answer: (c) Both I and II. The matrix with $a_{ij} = 1$ for $i = j$ and 0 otherwise is the identity matrix $I_3$. All entries below the diagonal are 0, so it is upper triangular (Statement I is true), and $|I_3| = 1$ (Statement II is true).