## 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 3A^{2} – 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^{T}A^{T}

Solution:

From (i) and (iv),(AB)^{T} = B^{T}A^{T}

Hence Proved.

Question 8.

Prove that

Solution:

= (ax + hy + gz)x + (hx + by + fz)v + (gr + fy + cz)z

= ax^{2} + hxy + gzx + hxy + by^{2} + fyz + gzx + fyz + cz^{2}

= ax^{2} + by^{2} + cz^{2} + 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} = A^{2} + B^{2}, 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 A^{2} = 8A + KI.

Solution:

Let A^{2} = 8A + KI

Question 14.

, then find A.

Solution:

Question 15.

Solution:

##### RBSE Solutions for Class 12 Maths

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