Matrices questions
472 published questions with worked solutions.
- Let A= bmatrix 0&1&0 1&0&0 0&0&1 bmatrix . Then the number of 3×3 matrices B with entries from the set 1, 2, 3, 4, 5 and...
- Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear...
- Let M be any 3 × 3 matrix with entries from the set 0, 1, 2 . The maximum number of such matrices, for which the sum of diagonal...
- How many 3 3 matrices M with entries from 0,1,2 are there, for which the sum of the diagonal entries of M^TM is 5?
- Let a,b and c be three real numbers satisfying bmatrix a&b&c bmatrix bmatrix 4&7&3 7&4&3 6&5&3 bmatrix = bmatrix 0&0&0 bmatrix ....
- Let A = bmatrix 1&2 -1&4 bmatrix . If A^ -1 = I+ A, , R, I is a 2 × 2 identity matrix, then 4( - ) is equal to :
- For real numbers and , consider the following system of linear equations : x+y-z=2, x+2y+ =1, 2x-y+z= . If the system has...
- Let A and B be two 3 × 3 real matrices such that (A^2-B^2) is invertible matrix. If A^5=B^5 and A^3B^2=A^2B^3, then the value of...
- If A= bmatrix 1&0&1 0&1&1 0&0&1 bmatrix and M = A + A^2 + A^3 + .... + A^ 20 then the sum of all the elements of the matrix M is...
- If the matrix A = pmatrix 0&2 &-1 pmatrix satisfies A(A^3+3I) = 2I, then the value of K is :
- If the system of linear equations 2x + y – z = 3, x – y – z = , 3x + 3y + = 3 has infinitely many solution, then + - is equal to...
- Let [ ] be the greatest integer less than or equal to . The set of all values of for which the system of linear equations x + y +...
- Let A be a 3 × 3 matrix with det(A) = 4. Let R_i denote the i^ th row of A. If a matrix B is obtained by performing the operation...
- If for the matrix, A= bmatrix 1&- & bmatrix , AA^T=I_2, then the value of ^4+ ^4 is :
- Let A = bmatrix x&y&z &z&x &x&y bmatrix , where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If A^2=I_3, then...
- Let S= n N: pmatrix 0&i 1&0 pmatrix ^n pmatrix a&b &d pmatrix ^n= pmatrix a&b &d pmatrix a,b,c,d R , where i= -1 . Then the...
- Let A= pmatrix 1&0&0 0&1&1 1&0&0 pmatrix . Then A^ 2025 -A^ 2020 is equal to:
- If A= pmatrix 1 5 & 2 5 -2 5 & 1 5 pmatrix , B= pmatrix 1&0 &1 pmatrix , i= -1 , and Q = A^TBA, then the inverse of the matrix...
- If the matrix A= bmatrix 1&0&0 0&2&0 3&0&-1 bmatrix satisfies the equation A^ 20 + A^ 19 + A= bmatrix 1&0&0 0&4&0 0&0&1 bmatrix...
- Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A^2 is 1, then the possible...
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