Exams › JEE Main › Maths

For positive numbers x, y and z, evaluate the determinant of the matrix with rows [1, logₓ y, logₓ z], [log_y x, 1, log_y z], [log_z x, log_z y, 1].

1. 0
2. log(xyz)
3. log(x + y + z)
4. (log x)(log y)(log z)

Correct answer: 0

Solution

Converting to a common base, each row becomes proportional to (log x, log y, log z), so two rows are linearly dependent and the determinant is 0.

Related JEE Main Maths questions

• If [ ] represents the greatest integer less than or equal to the given real number, and -1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, then the determinant [x] [y] [z] [x+1] [y+1] [z] [x] [y] [z]+1 is equal to:
• Let x, y and z be complex numbers. If Δ denotes the determinant of the matrix [0, -y, -z; y, 0, -x; z, x, 0], then Δ is
• For the linear system x1 + 2x2 + 3x3 = 6 x1 + 3x2 + 5x3 = 9 2x1 + 5x2 + ax3 = b if it is consistent and admits infinitely many solutions, then which statement must be true?
• For which value(s) of x does the determinant of the matrix | 1 (x−3) (x−3)² | | 1 (x−4) (x−4)² | | 1 (x−5) (x−5)² | become zero?
• Let Δ_r denote the determinant [2r-1, {^mC_r}, 1; m²-1, 2^m, m+1; sin²(m²), sin²(m), sin²(m+1)]. Then the value of ∑_(r=0)^(m) Δ_r is
• If the determinant expression [a, b, ax+by; b, c, bx+cy; ax+by, bx+cy, 0] is considered under the conditions b²-ac<0 and a<0, what is its sign?

⚔️ Practice JEE Main Maths free + battle 1v1 →