Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If $straight A subscript alpha$ = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ , then which of following statement is true -

$A_{α}$ . $A_{β}$ = $A_{α + β}$ and( $A_{α}$ )n = $[\begin{matrix} \cos^{n} α & \sin^{n} α \\ - \sin^{n} α & \cos^{n} α \end{matrix}]$
$A_{α}$ $A_{β}$ = $A_{α + β}$ and( $A_{α}$ )n = $[\begin{matrix} \cos n α & \sin n α \\ - \sin n α & \cos n α \end{matrix}]$
$A_{α}$ . $A_{β}$ = $A_{α + β}$ and( $A_{α}$ )n = $[\begin{matrix} \cos^{n} α & \sin^{n} α \\ - \sin^{n} α & \cos^{n} α \end{matrix}]$
$A_{α}$ . $A_{β}$ = $A_{α + β}$ and( $A_{α}$ )n = $[\begin{matrix} \cos n α & \sin n α \\ - \sin n α & \cos n α \end{matrix}]$

The correct answer is: $straight A subscript alpha$ . $straight A subscript beta$ = $A subscript alpha plus beta end subscript$ and( $straight A subscript alpha$ )n = $open square brackets table row cell cos invisible function application n alpha end cell cell sin invisible function application n alpha end cell row cell negative sin invisible function application n alpha end cell cell cos invisible function application n alpha end cell end table close square brackets$

we are given matrix A and we are asked to find which of the given statements are true.
By using the properties of a matrix we verify that
$straight A subscript alpha$ . $straight A subscript beta$ = $A subscript alpha plus beta end subscript$ and( $straight A subscript alpha$ )n = $open square brackets table row cell cos invisible function application n alpha end cell cell sin invisible function application n alpha end cell row cell negative sin invisible function application n alpha end cell cell cos invisible function application n alpha end cell end table close square brackets$

Therefore the correct option is choice 4

Related Questions to study

If A = $open square brackets table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell 0 row cell sin invisible function application theta end cell cell cos invisible function application theta end cell 0 row 0 0 1 end table close square brackets$ , then -

If A = $open square brackets table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell 0 row cell sin invisible function application theta end cell cell cos invisible function application theta end cell 0 row 0 0 1 end table close square brackets$ , then -

If D = diag (d₁, d₂,.....,d_n), then Dⁿ equals -

If D = diag (d₁, d₂,.....,d_n), then Dⁿ equals -

If A = $open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets$ , then for every positive integer n, Aⁿ is equal to -

If A = $open square brackets table row 3 cell negative 4 end cell row 1 cell negative 1 end cell end table close square brackets$ , then for every positive integer n, Aⁿ is equal to -

parallel

If A = [aij] is scalar matrix of order n × n such that aij = k for all i, then |A| equals -

If A = [aij] is scalar matrix of order n × n such that aij = k for all i, then |A| equals -

If E ( $theta$ ) = $open square brackets table row cell cos invisible function application theta end cell cell sin invisible function application theta end cell row cell negative sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets$ then E( $alpha$ ) E( $beta$ ) is equal to-

If E ( $theta$ ) = $open square brackets table row cell cos invisible function application theta end cell cell sin invisible function application theta end cell row cell negative sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets$ then E( $alpha$ ) E( $beta$ ) is equal to-

When bleaching powder is treated with carbon dioxide:

When bleaching powder is treated with carbon dioxide:

chemistry-General

parallel

If A = $open square brackets table row 1 1 row 1 1 end table close square brackets$ and n $element of$ N, then Aⁿ is equal to-

If A = $open square brackets table row 1 1 row 1 1 end table close square brackets$ and n $element of$ N, then Aⁿ is equal to-

If A = $open square brackets table row 1 2 row cell negative 4 end cell cell negative 1 end cell end table close square brackets$ , then A^–1 =

If A = $open square brackets table row 1 2 row cell negative 4 end cell cell negative 1 end cell end table close square brackets$ , then A^–1 =

For any square matrix A, which statement is wrong-

For any square matrix A, which statement is wrong-

parallel

If A = $open square brackets table row 2 0 0 row 0 2 0 row 0 0 2 end table close square brackets$ , then value of A^–1 is-

If A = $open square brackets table row 2 0 0 row 0 2 0 row 0 0 2 end table close square brackets$ , then value of A^–1 is-

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = BX, then X equals -

If A = $open square brackets table row 1 2 row 3 cell negative 5 end cell end table close square brackets$ , B = $open square brackets table row 1 0 row 0 2 end table close square brackets$ and X is a matrix such that A = BX, then X equals -

Matrix $open square brackets table row lambda cell negative 1 end cell 4 row cell negative 3 end cell 0 1 row cell negative 1 end cell 1 2 end table close square brackets$ is not invertible if-

Matrix $open square brackets table row lambda cell negative 1 end cell 4 row cell negative 3 end cell 0 1 row cell negative 1 end cell 1 2 end table close square brackets$ is not invertible if-

parallel

Which acid on keeping for long time acquires brown colour?

Which acid on keeping for long time acquires brown colour?

chemistry-General

If A is a square matrix of order n, then the value of |adj A| is-

If A is a square matrix of order n, then the value of |adj A| is-

(adj A^T) – (adj A)^T equals-

(adj A^T) – (adj A)^T equals-

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.