# Exercise 4.2 (Q10 to Q16) Determinants Class 12 Maths Chapter 4

## Topics/Questions discussed in this video:

00:00:47 NCERT Solutions Exercise 4.2 Question 10 part (i) {\begin{vmatrix} {x + 4}&{2x}&{2x}\\ {2x}&{x + 4}&{2x}\\ {2x}&{2x}&{x + 4} \end{vmatrix} = (5x + 4){{(4 - x)}^2}}

00:05:57 NCERT Solutions Exercise 4.2 Question 10 part (ii) {\begin{vmatrix} {y + k}&y&y\\ y&{y + k}&y\\ y&y&{y + k} \end{vmatrix}} = {k^2}(3y + k)

00:08:47 NCERT Solutions Exercise 4.2 Question 11 part (i) {\begin{vmatrix} {a - b - c}&{2a}&{2a}\\ {2b}&{b - c - a}&{2b}\\ {2c}&{2c}&{c - a - b} \end{vmatrix}} = {(a + b + c)^3}

00:13:27 NCERT Solutions Exercise 4.2 Question 11 part (ii) {\begin{vmatrix} {x + y + 2z}&x&y\\ z&{y + z + 2x}&y\\ z&x&{z + x + 2y} \end{vmatrix}} = 2{(x + y + z)^3}

00:18:47 NCERT Solutions Exercise 4.2 Question 12 {\begin{vmatrix} 1&x&{{x^2}}\\ {{x^2}}&1&x\\ x&{{x^2}}&1 \end{vmatrix}} = {(1 - {x^3})^2}

00:21:37 NCERT Solutions Exercise 4.2 Question 13 {\begin{vmatrix} {1 + {a^2} - {b^2}}&{2ab}&{ - 2b}\\ {2ab}&{1 - {a^2} + {b^2}}&{2a}\\ {2b}&{ - 2a}&{1 - {a^2} - {b^2}} \end{vmatrix}} = {(1 + {a^2} + {b^2})^3}

00:29:17 NCERT Solutions Exercise 4.2 Question 14 {\begin{vmatrix} {{a^2} + 1}&{ab}&{ac}\\ {ab}&{{b^2} + 1}&{bc}\\ {ca}&{cb}&{{c^2} + 1} \end{vmatrix}} = 1 + {a^2} + {b^2} + {c^2}

00:35:37 NCERT Solutions Exercise 4.2 Question 15 Let A be a square matrix of order 3 × 3, then |k\,{\rm{A}}| is equal to
(A) k| A|
(B) {k^2}|{\rm{A}}|
(C) {k^3}|{\rm{A}}|
(D) 3k|{\rm{A}}|

00:36:17 NCERT Solutions Exercise 4.2 Question 16
Which of the following is correct
(A) Determinant is a square matrix.
(B) Determinant is a number associated to a matrix.
(C) Determinant is a number associated to a square matrix.
(D) None of these

00:37:27 Area of a triangle using determinants
00:40:17 NCERT Solutions Exercise 4.3 Question 1
Find area of the triangle with vertices at the point given in each of the following:
(i) (1, 0), (6, 0), (4, 3)
(ii) (2, 7), (1, 1), (10, 8)
(iii) (–2, –3), (3, 2), (–1, –8)

00:46:22 Prove points are collinear using area of triangle and determinants

00:47:02 NCERT Solutions Exercise 4.3 Question 2
Show that points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.

## Agam Sir

Teacher

Ashish Kumar a.k.a Agam Sir has vast experience of 12+ years of teaching Mathematics and Physics. He has skills (academic and vocational) that go with working alongside people, especially young people, their parent(s) and the institutes that works with him. He always seek to be an agent of positive change and progression, a mentor/ trainer/ educator for learners/students, seeing that their needs are ideally met.