Author name: Ankur Negi

Question 1: Evaluate Minors and Cofactors of the elements of the following determinant: (i) Solution: Element a₁₁ = 2 Element a₁₂ = -4 Element a₂₁ = 0 Element a₂₂ = 3 Summary Table: (ii) Solution: Element a₁₁ = a Element a₁₂ = c Element a₂₁ = b Element a₂₂ = d Summary Table: Question 2:

Question 1: Find the area of the triangle with vertices at the points given: (i) Solution:Using the formula for the area of triangle: Substituting the points: Expanding: (ii) Solution:Substituting the points: Expanding: (iii) Solution:Substituting the points: Expanding: Question 2: Show that points are collinear. Solution:If points are collinear the area of a triangle formed by

Evaluate the determinants in Exercises 1 and 2 Question 1: Solution: Question 2 (i) Solution: (ii) Solution: Question 3: If , Then show that Solution: Now, , Hence Proved Question 4: If , then show that |3A| = 27 |A| Solution: determinant of triangular matrix is product of diagonal elements: Now, This is an upper

Question 1: If and are symmetric matrices, prove that is a skew‑symmetric matrix. Solution: Because and are symmetric, their transposes equal themselves: and . Consider the transpose of : By definition, a matrix is skew‑symmetric when . Hence is skew‑symmetric. Question 2: Show that is symmetric or skew‑symmetric according as is symmetric or skew‑symmetric. Solution: Step 1 Recall

Question 1: Matrices A and B will be inverse of each other only if (A) (B) (C) , (D) Solution: Two square matrices of the same order, say and , are inverses of each other if and only if each is the multiplicative inverse of the other, i.e., This relation guarantees that both left‑ and

Question 1: Find the transpose of each of the following matrices: (i) (ii) (iii) Solution 1: (i) Let . Then (ii) Let . Then (iii) Let . Then Question 2 If and verify that(i) (ii) Solution 2 (i) Compute : Then Now compute : Thus (i) is verified. (ii) Compute : Then Thus (ii) is

Those of you looking for NCERT of Class 12 Maths Exercise 3.2, have reached the right place. This exercise covers topics like Addition of Matrices, Multiplication of a matrix by a scalar, Properties of Matrix Addition, Properites of Scalar multiplication of a matrix, multiplication of matrices, properties of multiplication of matrices this makes it essential