AP EAMCET202316 May 2023Morning ShiftMathematicsMatricesActual

In a matrix A , if all the sub matrices or k orcer are singular and there is one non-singular sub matrix of order r (r < k) , then the rank ( ) of the matrix A

Options

Asatisfies r < k
Bis equal to r
Cis equal to ( k -1)
Dis equal to ( k +1)

Correct answer

A. satisfies r < k

Step-by-step solution

Since, all the sub-matrices of k^ th order are singular. Rank of A= < k < k ...(i) Also, there is one non-singular sub matrix of order r . So, r Rank of A r ...(ii) From eqn. (1) and (11), we get r < k

Practice Matrices on Quantrex Academy →

More from Matrices

Given A = bmatrix x & 1 & -2 bmatrix and B = bmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 bmatrix . If ABA^t = [-20] then the value of x is: 2026 If the matrix M = bmatrix x+5 & a & -4 -2 & 0 & b c & 6 & y+1 bmatrix is a skew symmetric matrix, the value of the expression ab + c^2 - xy is: 2026 Matrix A = bmatrix 1 & 1 & 2 1 & -2 & 2 1 & 0 & -1 bmatrix , Given M₂₂ and A₃₂ are the minor and cofactor of the adjoint matrix of A respectively then the value of the expression M 2026 If A and B are two square matrices of the same order such that AB = A and BA = B , then (A + B)^2 is equal to: 2026 Given the matrices A = bmatrix 1 & 0 & 1 0 & 1 & 0 1 & 0 & 2 bmatrix and B = bmatrix 2 & 1 & 0 1 & 1 & 2 0 & 2 & 1 bmatrix , then the minor M₂₃ of the matrix (A B⁻¹)⁻¹ is: 2026 Given A = pmatrix 1 & 2 2 & 3 pmatrix and f(x) = x^2 - 2x - 3 then f(A) is: 2026 If the system of equations 2 x+p y+6 z=8, x+2 y+q z=5 and x+y+3 z=4 has infinitely many solutions, then p = 2025 If x^a y^b=e^m, x^c y^d=e^n, ₁= | array ll m & b n & d array |, ₂= | array ll a & m c & n array |, ₃= | array ll a & b c & d array | , then the values of x and y are respectively ( 2025 Full Matrices list All AP EAMCET PYQs