Question
The value of x for which the matrix A =
is inverse of B =
is
The correct answer is: ![fraction numerator 1 over denominator 5 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAIJJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CoZCDI4WZDQw6BcQfwLibUBcBMQ8lBjIAsTG0IbEDSDWoIYr3YD4ILW8/IMahugA8V1SNa0DYksgZoJiD6ghQaQaFArEt4D4DxC/A+JVQGyKTwMAfKc5il4VJDgAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+NTwvbW4+PC9tZnJhYz48L21hdGg+Xdkl9QAAAABJRU5ErkJggg==)
We have
AB =
= ![open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets](data:image/png;base64,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)
x = 1/5
Related Questions to study
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 .![for all straight i times not equal to straight j](data:image/png;base64,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)
Statement I :
is a diagonal matrix.
Statement II : A square matrix A = (aij) is a diagonal matrix if aij = 0 .![for all straight i times not equal to straight j](data:image/png;base64,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)
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 A
I 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 A
I 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. [![because](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC)
= 0, since R2 = 2R1]
Assertion (A): The inverse of the matrix
does not exist.
Reason (R) : The matrix
is singular. [![because](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACRJREFUeNpjYMAE/6EYGwiAyi1nIACoYsgoIAzwBTR9DaEPAABHCgvlC8PdSAAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIzNTs8L21vPjwvbWF0aD6HYN/sAAAAAElFTkSuQmCC)
= 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 ![open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets](data:image/png;base64,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)
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 ![open square brackets table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close square brackets](data:image/png;base64,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)
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) .