Case study problem matrix 2 chapter 3 class 12

Case study Chapter 3 (Matrix)

Case study 2:- Amit, Biraj and chirag were giventhe task of creating a square matrix of order 2. Below are the matrices created by them. A, B, C are the matrices created by Amit, Biraj and Chirag respectively.(Case study problem matrix 2)

Case study problem matrix 2 — Amit, Biraj and chirag were giventhe task of creating a square matrix of order 2

$A=\begin{bmatrix} 1& 2\\-1 & 3\end{bmatrix}, B= \begin{bmatrix} 4& 0\\1 & 5\end{bmatrix}$

$C= \begin{bmatrix} 2 & 0\\1 & -2\end{bmatrix}$

If a = 4 and b = -2

Based on the above information answer the following question.

(i) (a) Find the sum of the matrices A, B and C, A+(B+C).

(b) Evaluate $(A^T)^T$ .

(ii) (a) Find th matrices AC – BC.

(b) Find the matrix of (a + b)B.

Solution (i) (a) We have,

$A + (B + C) = \begin{bmatrix} 1& 2\\-1 & 3\end{bmatrix} + \left(\begin{bmatrix} 4& 0\\1 & 5\end{bmatrix} + \begin{bmatrix} 2 & 0\\1 & -2\end{bmatrix}\right)$

$= \begin{bmatrix} 1& 2\\-1 & 3\end{bmatrix} + \begin{bmatrix} 6& 0\\2 & 3\end{bmatrix}$

$= \begin{bmatrix} 7& 2\\1 & 6\end{bmatrix}$

(b) We have

$A^T = \begin{bmatrix} 1& 2\\-1 & 3\end{bmatrix}^T$

$\Rightarrow A^T = \begin{bmatrix} 1& -1\\2 & 3\end{bmatrix}$

$(A^T)^T = \begin{bmatrix} 1& -1\\2 & 3\end{bmatrix}^T$

$= \begin{bmatrix} 1& 2\\-1 & 3\end{bmatrix} = A$

(ii) (a) we have,

$AC-BC = \begin{bmatrix} 1& 2\\-1 & 3\end{bmatrix}\begin{bmatrix} 2 & 0\\1 & -2\end{bmatrix}- \begin{bmatrix} 4& 0\\1 & 5\end{bmatrix}\begin{bmatrix} 2 & 0\\1 & -2\end{bmatrix}$

$= \begin{bmatrix} 4& -4\\1 & -6\end{bmatrix}-\begin{bmatrix} 10& 0\\-6 & 4\end{bmatrix}$

$= \begin{bmatrix} -4& -4\\-6 & 4\end{bmatrix}$

(b) We have,

$(a + b)B = (4 - 2)\begin{bmatrix} 4& 0\\1 & 5\end{bmatrix}$

$\Rightarrow (a + b)B = 2\begin{bmatrix} 4& 0\\1 & 5\end{bmatrix}$

$= \begin{bmatrix} 8& 0\\2 & 10\end{bmatrix}$

Case study 1:- Read the following and answer the question(Case study problem matrix 1)

A manufacturer produces three stationery products Pencil, Eraser and Sharpner which he sells in two markets. Annual sales are indicated below

Solution: For solution click here

Case study 3:- Read the following and answer the question:(Case study problem matrix 3)

Three schools DPS, CVC and KVS decided to organize a fair for collecting money for helping the flood victims. They sold Handmade fans, Mats and plates from recycled material at a cost of ₹25, ₹ 100 and ₹50 each respectively. The number of articles sold are given as.

Solution: For solution click here

Case study problem determinant 4 — On the occasion of children’s day. Class teacher of class XII shri singh,

Case study application of derivative 4 — These days chinese and Indian troops are engaged in aggressive melee, face-offs skirmishes

Case study application of integral 2 — An architect designs a building whose lift (elevator ) is from outside of the building attached to the walls.

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