Matrices Class 12 Maths Chapter 3 Miscellaneous Exercise

Matrices Lecture 7

Friday, April 23, 2021

Agam Sir

Video Format

Topics/Questions discussed in this video:

00:00:58 NCERT Solutions Miscellaneous Exercise Question 4
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.

00:05:18 NCERT Solutions Miscellaneous Exercise Question 5
Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

00:11:28 NCERT Solutions Miscellaneous Exercise Question 6 Find the values of x, y, z if the matrix A\, = \, {\begin{bmatrix} 0&{2y}&z\\ x&y&{ - z}\\ x&{ - y}&z \end{bmatrix}} satisfy the equation {\rm{A'A = I}}.

00:16:28 NCERT Solutions Miscellaneous Exercise Question 7 For what values of x : {\begin{bmatrix} 1&2&1 \end{bmatrix}} {\begin{bmatrix} 1&2&0\\ 2&0&1\\ 1&0&2 \end{bmatrix}} {\begin{bmatrix} 0\\ 2\\ x \end{bmatrix}} = {\rm{O}}?

00:18:48 NCERT Solutions Miscellaneous Exercise Question 8 If A = {\begin{bmatrix} 3&1\\ { - 1}&2 \end{bmatrix}} , show that {A^2} - 5A + 7I = O.

00:20:58 NCERT Solutions Miscellaneous Exercise Question 9 Find x, if {\begin{bmatrix} x&{ - 5}&{ - 1} \end{bmatrix}} {\begin{bmatrix} 1&0&2\\ 0&2&1\\ 2&0&3 \end{bmatrix}} {\begin{bmatrix} x\\ 4\\ 1 \end{bmatrix}} = {\rm{O}}

00:23:28 NCERT Solutions Miscellaneous Exercise Question 10 A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below:
\begin{matrix} {\rm{Market}} & & & {\rm{Products}}\\ \,\,\,\,\,\,\,\begin{bmatrix} {\rm{I}}\\ {{\rm{II}}} \end{bmatrix} & & & \begin{bmatrix} {10000}&{2000}&{18000}\\ {6000}&{20000}&{8000} \end{bmatrix} \end{matrix}
(a) If unit sale prices of x, y and z are ₹ 2.50, ₹ 1.50 and ₹ 1.00, respectively, find the total revenue in each market with the help of matrix algebra.
(b) If the unit costs of the above three commodities are ₹ 2.00, ₹ 1.00 and 50 paise respectively. Find the gross profit.

00:35:28 NCERT Solutions Miscellaneous Exercise Question 11 Find the matrix X so that {\rm{X}} {\begin{bmatrix} 1&2&3\\ 4&5&6 \end{bmatrix}} = {\begin{bmatrix} { - 7}&{ - 8}&{ - 9}\\ 2&4&6 \end{bmatrix}}

Choose the correct answer in the following questions:

00:42:18 NCERT Solutions Miscellaneous Exercise Question 15 If A is square matrix such that {A^2} = A, then {(I + A)^3} - 7Ais equal to
(A) A
(B) I – A
(C) I
(D) 3A

00:45:08 NCERT Solutions Miscellaneous Exercise Question 14 If the matrix A is both symmetric and skew symmetric, then
(A) A is a diagonal matrix
(B) A is a zero matrix
(C) A is a square matrix
(D) None of these

00:46:48 NCERT Solutions Miscellaneous Exercise Question 13 If A = {\begin{bmatrix} \alpha &\beta \\ \gamma &{ - \alpha } \end{bmatrix}} is such that {{\rm{A}}^{\rm{2}}}{\rm{ = I}}, then
(A) 1 + {\alpha ^2} + \beta \gamma = 0
(B) 1 - {\alpha ^2} + \beta \gamma = 0
(C) 1 - {\alpha ^2} - \beta \gamma = 0
(D) 1 + {\alpha ^2} - \beta \gamma = 0

00:49:38 NCERT Solutions Miscellaneous Exercise Question 12 If A and B are square matrices of the same order such that AB = BA, then prove by induction that A{B^n} = {B^n}A. Further, prove that {(AB)^n} = {A^n}{B^n} for all n ∈ N.

Agam Sir

Agam Sir

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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.