Let A and B be 3 - 3 matrices such that A-A and B-B- Then matrix 3AB- BA is skew symmetric matrix for - equal to -

(3AB+λ BA)'=3(AB)'+λ (BA)' nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; =3B'A'+ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Engineering Mathematics

Symmetric, Skew-symmetric and Orthogonal Matrices

Let A and B b...

Question

$Let A and B be 3 \times 3 matrices such that A^{'} = - A and B^{'} = B . Then matrix 3 A B + λ B A is skew symmetric matrix for λ equal to______ .$
3

Open in App

Solution

The correct option is A 3
$(3 A B + λ B A)^{'} = 3 (A B)^{'} + λ (B A)^{'}$
$= 3 B^{'} A^{'} + λ A^{'} B^{'}$
$= - 3 B A - λ A B = - (λ A B + 3 B A)$
$λ = 3$

Suggest Corrections

Similar questions

Q. Figure shows two processes

A and B

on a system. Let

Δ Q_{1} and Δ Q_{2}

be the heat given to the system in processes

A and B

respectively. Then

Q. Two vectors

\to A and \to B

have equal magnitudes. The magnitude of

\to A + \to B

^{'} n^{'}

times the magnitude of

\to A - \to B

. The angle between

\to A and \to B

If six students, including two particular student $A a n d B$ , stand in a row, then the probability that $A a n d B$ are separated with one student in between them is

X $H_{2} S O_{4}$ +Y $S O_{2}$ +Z $N a_{2} C r o_{4}$ $⟶$ $C r_{2} (S O_{4})_{3}$ ) +A $N a_{2} S O_{4}$ +B $H_{2} O$ X,Y,Z,AandB are?

Q. Find the equivalent capacitance between

A and B

. All the capacitors have capacitance

C .

Join BYJU'S Learning Program

Let A and B be 3×3 matrices such that A′=−A and B′=B. Then matrix 3AB+λBA is skew symmetric matrix for λ equal to______ .3

The correct option is A 3(3AB+λBA)′=3(AB)′+λ(BA)′ =3B′A′+λA′B′ =−3BA−λAB=−(λAB+3BA) λ=3

$Let A and B be 3 \times 3 matrices such that A^{'} = - A and B^{'} = B . Then matrix 3 A B + λ B A is skew symmetric matrix for λ equal to______ .$
3

The correct option is A 3
$(3 A B + λ B A)^{'} = 3 (A B)^{'} + λ (B A)^{'}$
$= 3 B^{'} A^{'} + λ A^{'} B^{'}$
$= - 3 B A - λ A B = - (λ A B + 3 B A)$
$λ = 3$