Matrices questions
472 published questions with worked solutions.
- Let A be a matrix such that A bmatrix 1 & 2 0 & 3 bmatrix is a scalar matrix and |3A| = 108. Then A^2 equals
- Suppose A is any 3 × 3 non-singular matrix and (A – 3I) (A – 5I) = O, where I = I_3 and O = O_3. If A + A^ -1 = 4I, then + is...
- If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trivial solution (x, y, z), then x y + y...
- The total number of matrices A = pmatrix 0 & 2y & 1 2x & y & -1 2x & -y & 1 pmatrix , (x, y ∈ R, x ≠ y) for which A^TA = 3I_3 is:
- If the system of linear equations x + y + z = 5, x + 2y + 2z = 6, x + 3y + λz = μ, (λ, μ ∈ R), has infinitely many solutions,...
- If A = bmatrix e^t & e^ -t t & e^ -t t e^t & -e^ -t t - e^ -t t & -e^ -t t + e^ -t t e^t & 2e^ -t t & -2e^ -t t bmatrix then A is:
- If the system of linear equations x − 4y + 7z = g, 3y − 5z = h, −2x + 5y − 9z = k is consistent, then:
- If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = bmatrix 2 & 3 5 & -1 bmatrix , then AB is equal to:
- If B = bmatrix 5 & 2 & 1 0 & 2 & 1 & 3 & -1 bmatrix is the inverse of a 3 × 3 matrix A, then the sum of all values of α for which...
- Let P = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and Q = [q_ ij ] be two 3 × 3 matrices such that Q - P^5 = I_3. Then q_ 21...
- Let A = pmatrix 0 & 2q & r p & q & -r p & -q & r pmatrix . If AA^T = I_3, then |p| is:
- If the system of equations x + y + z = 5, x + 2y + 3z = 9, x + 3y + αz = β has infinitely many solutions, then β − α equals:
- If [x] denotes the greatest integer ≤ x, then the system of linear equations [sin θ]x + [−cos θ]y = 0, [cot θ]x + y = 0
- Let A=[a_ ij ] and B=[b_ ij ] be two 3 3 real matrices such that b_ ij =(3)^ (i+j-2) a_ ji , where i, j = 1, 2, 3. If the...
- The following system of linear equations 7x+6y-2z=0 3x+4y+2z=0 x-2y-6z=0, has
- If the matrices A = bmatrix 1 & 1 & 2 1 & 3 & 4 1 & -1 & 3 bmatrix , B = adj A and C = 3A, then | adj B| |C| is equal to :
- Let A be a 3 × 3 matrix such that adj A= bmatrix 2&-1&1 -1&0&2 1&-2&-1 bmatrix and B = adj (adj A). If |A| = and |(B^ -1 )^T|= ,...
- Let the system of equations x + 2y + 3z = 5, 2x + 3y + z = 9, 4x + 3y + λz = μ have infinite number of solutions. Then λ + 2μ is...
- Let A = I_2 − 2MM^T, where M is a real matrix of order 2 × 1 such that the relation M^TM = I_1 holds. If λ is a real number such...
- If the system of equations 2x + 3y − z = 5, x + αy + 3z = −4, 3x − y + βz = 7 has infinitely many solutions, then 13αβ is equal...
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