Matrices questions
472 published questions with worked solutions.
- Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M N^2 and M^2 = N^4, then
- Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if
- Let X and Y be two arbitrary, 3 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 3, non-zero, symmetric matrix. Then...
- Let P= bmatrix 1 & 0 & 0 4 & 1 & 0 16 & 4 & 1 bmatrix and I be the identity matrix of order 3. If Q=[q_ ij ] is a matrix such...
- Let a, , R . Consider the system of linear equations ax+2y= 3x-2y= Which of the following statement(s) is(are) correct?
- For a real number , if the system bmatrix 1 & & ^2 & 1 & ^2 & & 1 bmatrix bmatrix x y z bmatrix = bmatrix 1 -1 1 bmatrix of...
- 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 S be the set of all column matrices bmatrix b_1 b_2 b_3 bmatrix such that b_1,b_2,b_3 R and the system of equations (in real...
- Let M= bmatrix ^4 & -1- ^2 1+ ^2 & ^4 bmatrix = I+ M^ -1 , where = ( ) and = ( ) are real numbers, and I is the 2 2 identity...
- Let M= bmatrix 0 & 1 & a 1 & 2 & 3 3 & b & 1 bmatrix and adj ,M= bmatrix -1 & 1 & -1 8 & -6 & 2 -5 & 3 & -1 bmatrix where a and b...
- Let P_1=I= bmatrix 1&0&0 0&1&0 0&0&1 bmatrix , P_2= bmatrix 1&0&0 0&0&1 0&1&0 bmatrix , P_3= bmatrix 0&1&0 1&0&0 0&0&1 bmatrix ,...
- What is [x y z] bmatrix a&h&g &b&f &f&c bmatrix equal to?
- If m= bmatrix 1&0 0&1 bmatrix and n= bmatrix 0&1 -1&0 bmatrix , then what is the value of the determinant of m -n ?
- If f(x)= bmatrix x&- x&0 x& x&0 0&0&1 bmatrix , then which of the following are correct? 1. f( ) f( )=f( + ). 2. The value of the...
- If A= bmatrix 1&-1 2&3 bmatrix and B= bmatrix 2&3 -1&-2 bmatrix , then which of the following is/are correct? 1. AB(A^ -1 B^ -1 )...
- If A= bmatrix & - & bmatrix then what is AA^T equal to (where A^T is the transpose of A)?
- The equations x+2y+3z=1, 2x+y+3z=2, 5x+5y+9z=4
- A= bmatrix x+y&y &x-y bmatrix , B= bmatrix 3 -2 bmatrix and C= bmatrix 4 -2 bmatrix . If AB=C, then what is A^2 equal to?
- Consider the set A of all matrices of order 3 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices...
- If A= bmatrix & - & bmatrix , then what is A^3 equal to?
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