3 questions from 2023
Let \( \alpha, \beta \) and \( \gamma \) be real numbers. Consider the following system of linear equations\( x + 2y + z = 7 \) \( x + \alpha z = 11 \) \( 2x - 3y + \beta z = \gamma \) Match each entry in List-I to the correct entries in List-II.
The correct option is:
Let \( M=(a_{ij}),\, i,j\in\{1,2,3\} \), be the \( 3\times3 \) matrix such that \( a_{ij}=1 \) if \( j+1 \) is divisible by \( i \), otherwise \( a_{ij}=0 \). Then which of the following statements is(are) true?
Then the number of invertible matrices in \( R \) is:
