Question
The greatest possible difference between two of the roots if [0, 2
] is
- 2
- 1
![square root of 2](data:image/png;base64,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)
- 2
![square root of 2](data:image/png;base64,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)
The correct answer is: 2
Related Questions to study
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) .