# 43 Lecture

## CS201

### Midterm & Final Term Short Notes

## Programming Exercise - Matrices

Matrices are rectangular arrays of numbers that can be used to represent mathematical equations or data. Programming exercises involving matrices often involve tasks such as matrix multiplication, addition, or finding the determinant. These exer

**Important Mcq's**

Midterm & Finalterm Prepration

Past papers included

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**What is a matrix in programming?**A. A tool used for debugging code B. A rectangular array of numbers C. A type of conditional statement D. A data structure used for storing strings

Answer: B. A rectangular array of numbers

**What is the process of adding two matrices called?**A. Multiplication B. Subtraction C. Addition D. Division

Answer: C. Addition

**Which data structure is commonly used for representing matrices in programming?**A. Stack B. Queue C. Array D. Linked list

Answer: C. Array

**What is the result of multiplying a 3x2 matrix with a 2x3 matrix?**A. A 3x3 matrix B. A 3x2 matrix C. A 2x3 matrix D. A 2x2 matrix

Answer: A. A 3x3 matrix

**What is the identity matrix?**A. A matrix with zeros in all its elements B. A matrix with ones in all its elements C. A matrix with zeros in all its diagonal elements and ones in all its other elements D. A matrix with ones in all its diagonal elements and zeros in all its other elements

Answer: D. A matrix with ones in all its diagonal elements and zeros in all its other elements

**Which of the following is used for finding the determinant of a matrix?**A. Gaussian elimination B. LU decomposition C. QR decomposition D. Singular value decomposition

Answer: A. Gaussian elimination

**Which of the following is true about a symmetric matrix?**A. It has equal number of rows and columns B. It is a square matrix C. It is equal to its transpose D. It has only positive numbers as its elements

Answer: C. It is equal to its transpose

**What is the inverse of a matrix?**A. A matrix with all its elements multiplied by -1 B. A matrix with all its elements squared C. A matrix that when multiplied by the original matrix gives the identity matrix D. A matrix with all its elements equal to the reciprocal of the original matrix

Answer: C. A matrix that when multiplied by the original matrix gives the identity matrix

**Which of the following operations is not possible with matrices?**A. Addition B. Subtraction C. Multiplication D. Division

Answer: D. Division

**Which of the following is used for solving systems of linear equations represented by matrices?**A. Gaussian elimination B. LU decomposition C. QR decomposition D. Singular value decomposition

Answer: A. Gaussian elimination

**Subjective Short Notes**

Midterm & Finalterm Prepration

Past papers included

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**What is the difference between a square matrix and a rectangular matrix?**A square matrix has an equal number of rows and columns, while a rectangular matrix has different numbers of rows and columns.**What is the process of multiplying two matrices called, and how is it performed?**Matrix multiplication is the process of multiplying two matrices by taking the dot product of each row of the first matrix with each column of the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.**What is the transpose of a matrix?**The transpose of a matrix is the matrix obtained by interchanging its rows and columns.**What is the determinant of a matrix, and how is it calculated?**The determinant of a matrix is a scalar value that can be calculated using various methods, including Gaussian elimination, cofactor expansion, and LU decomposition. It is used to determine the invertibility of a matrix.**What is a diagonal matrix?**A diagonal matrix is a square matrix in which all the off-diagonal elements are zero.**What is the difference between a symmetric matrix and a skew-symmetric matrix?**A symmetric matrix is a matrix that is equal to its transpose, while a skew-symmetric matrix is a matrix whose transpose is equal to the negative of the original matrix.**What is an identity matrix?**An identity matrix is a square matrix in which all the diagonal elements are equal to one and all the off-diagonal elements are equal to zero.**What is an upper triangular matrix?**An upper triangular matrix is a square matrix in which all the elements below the main diagonal are zero.**What is the inverse of a matrix, and how is it calculated?**The inverse of a matrix is a matrix that, when multiplied by the original matrix, gives the identity matrix. It can be calculated using various methods, including Gauss-Jordan elimination and LU decomposition.**What are some practical applications of matrices in programming?**Matrices are used in various applications such as image processing, 3D graphics, machine learning, and numerical simulations. They can also be used to represent data in a tabular format.