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If A = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ , then A² equals-

$[\begin{matrix} \cos 2 α & \sin 2 α \\ - \sin 2 α & \cos 2 α \end{matrix}]$
$[\begin{matrix} \cos 2 α & - \sin 2 α \\ \sin 2 α & \cos 2 α \end{matrix}]$
$[\begin{matrix} \sin 2 α & \cos 2 α \\ - \cos 2 α & \sin 2 α \end{matrix}]$
$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

The correct answer is: $open square brackets table row cell cos invisible function application 2 alpha end cell cell sin invisible function application 2 alpha end cell row cell negative sin invisible function application 2 alpha end cell cell cos invisible function application 2 alpha end cell end table close square brackets$

To find the value of $A squared$ for the given matrix A.

Given A = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ .
$A squared$ = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ x $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$
= $open square brackets table row cell cos invisible function application 2 alpha end cell cell sin invisible function application 2 alpha end cell row cell negative sin invisible function application 2 alpha end cell cell cos invisible function application 2 alpha end cell end table close square brackets$

Therefore, using matrix multiplication, $A squared$ = = $open square brackets table row cell cos invisible function application 2 alpha end cell cell sin invisible function application 2 alpha end cell row cell negative sin invisible function application 2 alpha end cell cell cos invisible function application 2 alpha end cell end table close square brackets$

The root of the equation [x 1 2] $open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell 0 1 1 end cell row cell 1 0 1 end cell row cell 1 1 0 end cell end table close square brackets$ $open square brackets table row x row cell negative 1 end cell row 1 end table close square brackets$ = 0 is-

Maths-General

General

Maths-

If A = $open square brackets table row 3 1 row 7 5 end table close square brackets$ and A² + kI = 8A, then k equals

Maths-General

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Maths-

If A and B are matrices of order m × n and n × n respectively, then which of the following are defined-

Maths-General

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chemistry-

The multiplicative inverse of A = $open square brackets table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell row cell sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets$ is

maths-General

General

chemistry-

(A) and (B) are:

chemistry-General

General

maths-

A = $open square brackets table row 1 2 2 row 2 1 2 row 2 2 1 end table close square brackets$ , then A³ – 4A² – 6A is equal to -

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General

maths-

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

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maths-

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

maths-General

General

maths-

The value of x for which the matrix product $open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 2 0 7 row 0 1 0 row 1 cell negative 2 end cell 1 end table close square brackets$ $open square brackets table row cell – x end cell cell 14 x end cell cell 7 x end cell row 0 1 0 row x cell – 4 x end cell cell – 2 x end cell end table close square brackets$ equal an identity matrix is :

maths-General

General

maths-

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

maths-General

General

maths-

If A is a singular matrix, then adj A is :

maths-General

General

Maths-

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason.

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

Maths-General

In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason.

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If A =, then A2 equals-

The correct answer is:

To find the value of for the given matrix A.Given A =. = x =Therefore, using matrix multiplication, = =

Related Questions to study

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If A = and A2 + kI = 8A, then k equals

If A = and A2 + kI = 8A, then k equals

If A and B are matrices of order m × n and n × n respectively, then which of the following are defined-

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the products (A) and (B) are:

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A matrix A = (aij) m x n is said to be a square matrix if-

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A = , then A3 – 4A2 – 6A is equal to -

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If A = and A2 – 4A – n I = 0, then n is equal to

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If A = , then A–1 is equal to :

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If A is a singular matrix, then adj A is :

If A is a singular matrix, then adj A is :

Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.Statement - II The maximum value of sin x + cos x occurs when x =

Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.Statement - II The maximum value of sin x + cos x occurs when x =

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If A = $open square brackets table row 3 1 row 7 5 end table close square brackets$ and A² + kI = 8A, then k equals

If A = $open square brackets table row 3 1 row 7 5 end table close square brackets$ and A² + kI = 8A, then k equals

For any square matrix A = [aij], aij = 0, when i $not equal to$ j, then A is-

For any square matrix A = [aij], aij = 0, when i $not equal to$ j, then A is-

A = $open square brackets table row 1 2 2 row 2 1 2 row 2 2 1 end table close square brackets$ , then A³ – 4A² – 6A is equal to -

A = $open square brackets table row 1 2 2 row 2 1 2 row 2 2 1 end table close square brackets$ , then A³ – 4A² – 6A is equal to -

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

Inverse of the matrix $open square brackets table row 3 cell – 2 end cell cell – 1 end cell row cell – 4 end cell 1 cell – 1 end cell row 2 0 1 end table close square brackets$ is

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

If A = $open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets$ and A² – 4A – n I = 0, then n is equal to

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

If A = $open square brackets table row 1 2 row 3 5 end table close square brackets$ , then A^–1 is equal to :

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$

Statement - I The value of x for which (sin x + cos x)^{1 + sin 2x} = 2, when 0 ≤ x ≤ , is $straight pi divided by 4$ only.
Statement - II The maximum value of sin x + cos x occurs when x = $straight pi divided by 4$