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Case Study Questions for Class 12 Maths Chapter 3 Matrices

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Case Study Questions for Class 12 Maths Chapter 3 Matrices

Case Study Questions:

Question 1:

A company produces three products every day. Their production on certain day is 45 tons. It is found that the production of third product exceeds the production of first product by 8 tons while the total production of first and third product is twice the production of second product. Using the concepts of matrices and determinants, answer the following questions:

(i) If x, y and z respectively denote the quantity (in tons) of first, second and third product produced, then which of the following is true?
(a) x + y + z = 45
(b) x + 8 = z
(c) x – 2y + z = 0
(d) All of these

(ii) If $$\left(\begin{array}{ccc}1 & 1 & 1 \\ 1 & 0 & -2 \\ 1 & -1 & 1\end{array}\right)^{-1}=\frac{1}{6}\left(\begin{array}{ccc}2 & 2 & 2 \\ 3 & 0 & -3 \\ 1 & -2 & 1\end{array}\right),$$ then the inverse of $$\left(\begin{array}{ccc}1 & 1 & 1 \\ 1 & 0 & -1 \\ 1 & -2 & 1\end{array}\right)$$ is
(a) $$\left[\begin{array}{ccc}\frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{2} & 0 & \frac{-1}{2} \\ \frac{1}{6} & \frac{-1}{3} & \frac{1}{6}\end{array}\right]$$ (b) $$\left[\begin{array}{ccc}\frac{1}{2} & 0 & -\frac{1}{2} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{6} & \frac{-1}{3} & \frac{1}{6}\end{array}\right]$$ (c) $$\left[\begin{array}{ccc}\frac{1}{3} & \frac{1}{2} & \frac{1}{6} \\ \frac{1}{3} & 0 & \frac{-1}{3} \\ \frac{1}{3} & \frac{-1}{2} & \frac{1}{6}\end{array}\right]$$ (d) none of these

(iii) x : y : z is equal to
(a) 12 : 13 : 20
(b) 11 : 15 : 19
(c) 15 : 19 : 11
(d) 13 : 12 : 20

(iv) Which of the following is not true?
(a) |A| = |A′|
(b) (A′)–1 = (A–1)′
(c) A is skew-symmetric matrix of order 3 then |A| = 0
(d) |AB| = |A| + |B|

Show Answer Answer:
(i) d
(ii) c
(iii) b
(iv) d

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