Let A be the set of all 3 × 3 symmetric matrices all of whose entries are either 0 or 1 …
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Let A be the set of all 3 × 3 symmetric matrices all of whose entries are either 0 or 1 . Five of these entries are 1 and four of them are 0 .
The number of matrices A in A for which the system of linear equations \[A\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right]\] is inconsistent, is
The number of matrices A in A for which the system of linear equations \[A\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right]\] is inconsistent, is
- 0
- more than 2
- 2
- 1
Answer
(C) 2
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Consider the set A of all determinants of order 3 with entries 0 or 1. Let B be the subset of A consisting of…
- 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 …
- Consider the matrix P = ( array lll 2 & 0 & 0 0 & 2 & 0 0 & 0 & 3 array ) . Let the transpose of a matrix X…
- Let ax 7 + bx 6 + cx 5 + dx 4 + ex 3 + fx 2 + gx + h = | array ccc ( x +1) & ( x ^ 2 +2 ) & ( x ^ 2 + x ) ( x…
- If f(x)= | array ccc 2 x & 2 x & 2 x - x & x & - x x & x & x array | , then
- Let 0 (x, )= | array ccc x & & - & -x & 1 & 1 & x array | then
- If E(θ) = [ array cc ^ 2 & & ^ 2 array ] and θ and φ differ by an odd multiple of π/2, then E(θ). E(φ) is a
- If x N and ^ x C _ i , ^ x ^ 2 C _ i and x^ 3 C_ i , (i = 1, 2, 3) are binomial coefficients, then 12 | array…
More Matrices and Determinants questions · Browse all practice questions