Last Updated on July 29, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 12 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 12 maths. In this article, you will find case study questions for CBSE Class 12 Maths Chapter 3 Matrices. It is a part of Case Study Questions for CBSE Class 12 Maths Series.

Chapter | Matrices |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 12 |

Subject | Maths |

Useful for | Class 12 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 12 Maths Chapterwise Case Study |

### Case Study Questions on Matrices

**Questions**

Passage 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

** Difficulty Level: **Medium

Ans. Option (d) is correct.

(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

** Difficulty Level: **Medium

Ans. Option (c) is correct.

**(iii) x : y : z is equal to**

(a) 12 : 13 : 20

(b) 11 : 15 : 19

(c) 15 : 19 : 11

(d) 13 : 12 : 20

** Difficulty Level: **Medium

Ans. Option (b) is correct.

**(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|

** Difficulty Level: **Medium

Ans. Option (b) is correct.

### Also check

- Matrices Class 12 Case Study Questions Maths Chapter 3
- Inverse Trigonometric Functions Class 12 Case Study Questions Maths Chapter 2
- Relations and Functions Class 12 Case Study Questions Maths Chapter 1

### Topics from which case study questions may be asked

- Definition of a matrix
- Types of matrices: row matrix, column matrix, zero matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and symmetric and skew-symmetric matrices
- Order of a matrix
- Properties of matrix addition and scalar multiplication
- Properties of matrix multiplication
- Transpose of a matrix and properties of transpose
- Symmetric and skew-symmetric matrices
- Elementary operations (Transformation) of a matrix
- Invertible matrices
- Adjoint and inverse of a matrix

A matrix is a rectangular arrangement of numbers (real or complex) or functions arranged in rows or columns.

Case study questions from the above given topic may be asked.

### Frequently Asked Questions (FAQs) on Matrices Case Study

#### Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

#### Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:**Read the problem carefully:** Understand the scenario and identify the mathematical concepts involved.**Break down the problem:** Divide the case study into smaller parts to manage the information better.**Apply relevant formulas and theorems:** Use the appropriate mathematical tools to solve each part of the problem.

#### Q3: Why are case study questions included in the Class 12 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

#### Q4: What is a matrix?

A4: A matrix is a rectangular arrangement of numbers (real or complex) or functions arranged in rows or columns.

#### Q5: What are the types of matrices?

A5: There are several types of matrices, including:Row matrix: A matrix with a single row.**Column matrix: **A matrix with a single column.**Zero matrix: **A matrix in which all elements are zero.**Square matrix: **A matrix with the same number of rows and columns.**Diagonal matrix:** A square matrix in which all off-diagonal elements are zero.**Scalar matrix:** A diagonal matrix in which all diagonal elements are the same.**Identity matrix: **A diagonal matrix in which all diagonal elements are one.**Symmetric matrix: **A square matrix that is equal to its transpose.**Skew-symmetric matrix: **A square matrix that is equal to the negative of its transpose.

#### Q6: How do you add two matrices?

A6: Two matrices of the same order can be added by adding their corresponding elements.

#### Q7: **Are there any online resources or tools available for practicing **Matrices **case study questions?**

A7: We provide case study questions for CBSE Class 12 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.