RBSE Solutions for Class 12 Maths Chapter 3 Matrix Ex 3.2

Rajasthan Board RBSE Class 12 Maths Chapter 3 Matrix Ex 3.2

Question 1.

then find A+B and A – B.
Solution:
Given,

Question 2.
, then find matrix A and B.
Solution:

Question 3.
, then find C, where A + 2B + C = 0.
Solution:
Given,
A + 2B + C = O

Question 4.

then find 3A² – 2B.
Solution:
According to question,

Question 5.
, then show that AB ≠ BA.
Solution:

Hence, AB ≠ BA. Hence Proved.

Question 6.
, then show that: f(A)(B) = f(A + B).
Solution:

Question 7.
, then prove : (AB)^T = B^TA^T
Solution:



From (i) and (iv),(AB)^T = B^TA^T
Hence Proved.

Question 8.
Prove that

Solution:

= (ax + hy + gz)x + (hx + by + fz)v + (gr + fy + cz)z
= ax² + hxy + gzx + hxy + by² + fyz + gzx + fyz + cz²
= ax² + by² + cz² + 2hxy + 2fyz + 2gzx = R.H.S.
Hence Proved.

Question 9.
and ‘I’ is unit matrix of order 3 x 3, then prove

Solution:
Given,

Question 10.
, where O is zero matrix, then find a.
Solution:

Question 11.
, (A + B)² = A² + B², then find a, b.
Solution:
Given.

Question 12.

and I is unit matrix of order 2 x 2, then prove that

Solution:

Question 13.
, then find K, where A² = 8A + KI.
Solution:
Let A² = 8A + KI

Question 14.
, then find A.
Solution:

Question 15.

Solution:

RBSE Solutions for Class 12 Maths