Case study problem matrix 2 chapter 3 class 12

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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

Case study problem matrix 1
A manufacturer produces three stationery products Pencil, Eraser

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.

Case study problem matrix 3
Three schools DPS, CVC and KVS decided to organize a fair for collecting money

Solution: For solution click here

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