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 A = $open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets$ and (aI₂ + bA)² = A, then -

a = b = $\sqrt{2}$
a = b = 1/ $\sqrt{2}$
a = b = $\sqrt{3}$
a = b = 1/ $\sqrt{3}$

The correct answer is: a = b = 1/ $square root of 2$

we are given that A = $open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets$ and (aI2 + bA)2 = A, then we need to find the correct option
$left parenthesis a I plus b A right parenthesis squared space space equals left parenthesis a I plus b A right parenthesis left parenthesis a I plus b A right parenthesis space equals a squared I squared space plus a b I A plus b a A I plus b squared A squared space space space equals a squared I plus 2 a b A plus b squared space A squared space space left parenthesis because I space squared equals I comma I A equals A I right parenthesis space equals a squared I plus 2 a b A minus b squared space I left parenthesis because A space space 2 space space equals negative I right parenthesis space equals left parenthesis a squared minus b squared space right parenthesis I plus 2 a b A space E q u a t i n g space c o r r e s p o n d i n g space e l e m e n t s space i n space left parenthesis a I plus b A right parenthesis squared space space a n d space A squared space comma space w e space g e t space a squared minus b squared space space equals 0 space a n d space 2 a b equals 1 space s o l v i n g space t h i s space w e space g e t space a equals b equals plus-or-minus space fraction numerator 1 over denominator root index blank of 2 end fraction$

Therefore the correct option is choice 2

Related Questions to study

If A is invertible matrix, then det (A^–1) equals-

If A is invertible matrix, then det (A^–1) equals-

If D = diag (d₁, d₂, d₃, ...,d_n), where d₁ $not equal to$ 0 for all i = 1,2,....,n; then D^–1 is equal to-

If D = diag (d₁, d₂, d₃, ...,d_n), where d₁ $not equal to$ 0 for all i = 1,2,....,n; then D^–1 is equal to-

If A and B are square matrices such that AB = B and BA = A, then A² + B² is equal to-

If A and B are square matrices such that AB = B and BA = A, then A² + B² is equal to-

parallel

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 -

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 -

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 -

parallel

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 -

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-

parallel

When bleaching powder is treated with carbon dioxide:

When bleaching powder is treated with carbon dioxide:

chemistry-General

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 =

parallel

For any square matrix A, which statement is wrong-

For any square matrix A, which statement is wrong-

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 -

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.