Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

For two 3×3 matrices A and B , let A + B = 2B’ and 3A + 2B = I3 where B’ is the transpose of B and I3is 3×3 identity matrix . Then
A) 5A+10B=2I3
B) 3A+6B=2I3
C) 10A+5B=3I3
D) B+2A=I3

Answer
VerifiedVerified
486k+ views
like imagedislike image
Hint:
Taking transposes on the given equations we get 3A+2B=I3 and A=2BB and simplifying further we get that A = B and I3= 5A and using these values we can get the equation which satisfies these equations.

Complete step by step solution:
We are given that A + B = 2B’
Applying transpose on both sides
(A+B)=(2B)
We know that (A+B)=A+B and (A)=A
From this we get ,
 A+B=2BA=2BB
We are given that 3A + 2B = I3
Applying transpose on both sides we get
(3A + 2B)=(I3)3A+2B=I3
Substitute the value of Ain the above equation
3(2BB)+2B=I36B3B+2B=I36BB=I3
We are given that A + B = 2B’
From this B=A+B2
Substitute this in the previous equation
6B(A+B2)=I312BAB=2I3
Substitute the value of I3from the given equation 3A + 2B = I3
12BAB=2(3A+2B)11BA=6A+4B7A=7BA=B
Substituting in 3A + 2B = I3we get
3A+2A=I35A=I3
Now we have A = B and I3= 5A
We have asked 5A +10B
5A+10B=5A+10A=15A=3×5A=3I3

Therefore the correct option is C.

Note:
1) In mathematics, a matrix (plural: matrices) is a rectangular table of cells of numbers, with rows and columns.
2) Every square dimension set of a matrix has a special counterpart called an "identity matrix". The identity matrix has nothing but zeroes except on the main diagonal, where there are all ones.
3) An inverse matrix is a matrix that, when multiplied by another matrix, equals the identity matrix.
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
Social scienceSocial science
ChemistryChemistry
MathsMaths
BiologyBiology
EnglishEnglish
₹41,000 (9% Off)
₹37,300 per year
Select and buy