JEE Advanced Matrices and Determinants questions
5 Mathematics questions on Matrices and Determinants as asked in JEE Advanced, newest first.
- Let S = \ A = beginpmatrix 0 & 1 & c \ 1 & a & d \ 1 & b & e endpmatrix : a,b,c,d,e ∈ \0,1\ and |A| ∈ \-1,1\ \, where |A| denotes the determinant of A. Then the number of elements in S is _______.
2024
- Let α and β be the distinct roots of the equation x^2 + x - 1 = 0. Consider the set T = \1, α, β\. For a 3 × 3 matrix M = (a_ij)_3× 3, define R_i = a_i1 + a_i2 + a_i3 and C_j = a_1j + a_2j + a_3j for i = 1,2,3 and j =…
2024
- Let M = (a_ij), i, j ∈ \1, 2, 3\, be the 3 × 3 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?
2023
- Let R = \ beginpmatrix a & 3 & b \ c & 2 & d \ 0 & 5 & 0 endpmatrix : a,b,c,d ∈ \0,3,5,7,11,13,17,19\ \. Then the number of invertible matrices in R is
2023
- Let α, β and γ be real numbers. Consider the following system of linear equations x + 2y + z = 7 x + α z = 11 2x - 3y + β z = γ Match each entry in List-I to the correct entries in List-II. List-I (P) If β = 1/2(7α - 3)…
2023
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