Question
If A –2B = and 2A – 3B = , then matrix B is equal to–
The correct answer is:
We have
B = (2A –3B) –2 (A –2B) = 2
Related Questions to study
The value of x for which the matrix A = is inverse of B = is
The value of x for which the matrix A = is inverse of B = is
The greatest possible difference between two of the roots if [0, 2] is
The greatest possible difference between two of the roots if [0, 2] is
Statement I : is a diagonal matrix.
Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .
Statement I : is a diagonal matrix.
Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .
Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity. Denote by tr(A), The sum of diagonal entries of A, Assume that A2 = I.
Statement-I :If AI and A– I, then det A= – 1
Statement-II : If A I and A – I then tr(A)0.
Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity. Denote by tr(A), The sum of diagonal entries of A, Assume that A2 = I.
Statement-I :If AI and A– I, then det A= – 1
Statement-II : If A I and A – I then tr(A)0.
Suppose , let x be a 2×2 matrix such that AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix
Suppose , let x be a 2×2 matrix such that AX = B
Statement-I : X is non singular & |x| = ±2
Statement-II : X is a singular matrix
If then is equal to
If then is equal to
Statement-I : If A & B are two 3×3 matrices such that AB = 0, then A = 0 or B = 0
Statement-II : If A, B & X are three 3×3 matrices such that AX = B, |A| 0, then X = A–1B
Statement-I : If A & B are two 3×3 matrices such that AB = 0, then A = 0 or B = 0
Statement-II : If A, B & X are three 3×3 matrices such that AX = B, |A| 0, then X = A–1B
Assertion (A): The inverse of the matrix does not exist.
Reason (R) : The matrix is singular. [ = 0, since R2 = 2R1]
Assertion (A): The inverse of the matrix does not exist.
Reason (R) : The matrix is singular. [ = 0, since R2 = 2R1]
Assertion (A): is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i j.
Assertion (A): is a diagonal matrix
Reason (R) : A square matrix A = (aij) is a diagonal matrix if aij = 0 for all i j.
Consider = – 1, where ai. aj + bi. bj + ci.cj = and i, j = 1,2,3
Assertion(A) : The value of is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0
Consider = – 1, where ai. aj + bi. bj + ci.cj = and i, j = 1,2,3
Assertion(A) : The value of is equal to zero
Reason(R) : If A be square matrix of odd order such that AAT = I, then | A + I | = 0
Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i j is B = [aij–1]n× n
Reason(R): The inverse of singular matrix does not exist
Assertion(A) : The inverse of the matrix A = [Aij]n × n where aij = 0, i j is B = [aij–1]n× n
Reason(R): The inverse of singular matrix does not exist
Assertion : The product of two diagonal matrices of order 3 × 3 is also a diagonal matrix
Reason : matrix multiplicationis non commutative
Assertion : The product of two diagonal matrices of order 3 × 3 is also a diagonal matrix
Reason : matrix multiplicationis non commutative
Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det = det (–)
Assertion : If A is a skew symmetric of order 3 then its determinant should be zero.
Reason : If A is square matrix then det A = det = det (–)
Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix
Reason : If A is non-singular then it commutes with I, adj A and A–1
Assertion : There are only finitely many 2 × 2 matrices which commute with the matrix
Reason : If A is non-singular then it commutes with I, adj A and A–1
Statement-I The equation has exactly one solution in [0, 2].
Statement-II For equations of type to have real solutions in should hold true.
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not , is same like assertion and reason. Here, Start solving first Statement and try to prove it . Then solve the Statement-II . Remember cos a cosb -sin a sinb = cos ( a + b ) and sin a cosb + cosa sinb = sin( a+ b) .
Statement-I The equation has exactly one solution in [0, 2].
Statement-II For equations of type to have real solutions in should hold true.
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not , is same like assertion and reason. Here, Start solving first Statement and try to prove it . Then solve the Statement-II . Remember cos a cosb -sin a sinb = cos ( a + b ) and sin a cosb + cosa sinb = sin( a+ b) .