Maths-
General
Easy
Question
If w is a complex cube root of unity, then the matrix A =
is a-
- singular matrix
- non-singular matrix
- skew symmetric matrix
- None of these
The correct answer is: singular matrix
We have
|A|=
=
[Using
]
=
= 0
A is a singular matrix.
Related Questions to study
maths-
Matrix [1 2]
is equal to-
Matrix [1 2]
is equal to-
maths-General
maths-
If A –2B =
and 2A – 3B =
, then matrix B is equal to–
If A –2B =
and 2A – 3B =
, then matrix B is equal to–
maths-General
maths-
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
maths-General
maths-
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
maths-General
maths-
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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)
maths-General
maths-
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.
maths-General
maths-
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
maths-General
maths-
If
then
is equal to
If
then
is equal to
maths-General
maths-
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
maths-General
maths-
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]
maths-General
maths-
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.
maths-General
maths-
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
maths-General
maths-
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
maths-General
maths-
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
maths-General
maths-
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 (–
)
maths-General