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FAQs on PPT - Matrices and Determinants - Business Mathematics and Statistics - B Com

1. What is a matrix and how is it used in mathematics?
Ans. A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is used in mathematics to represent and manipulate linear equations, systems of equations, transformations, and various other mathematical operations.
2. What is the purpose of determinants in matrix algebra?
Ans. Determinants are used in matrix algebra to provide important information about a matrix, such as whether it is invertible or singular. They also help in solving systems of linear equations, calculating areas and volumes, finding eigenvalues and eigenvectors, and performing various transformations.
3. How can matrices be multiplied together?
Ans. Matrices can be multiplied together using the dot product method. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in 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.
4. What is the process of finding the inverse of a matrix?
Ans. To find the inverse of a matrix, one can use the formula: inverse of A = 1/determinant of A * adjugate of A. The adjugate of a matrix is obtained by finding the transpose of the cofactor matrix. However, it is important to note that not all matrices have inverses. A matrix is invertible only if its determinant is non-zero.
5. How are determinants used in solving systems of linear equations?
Ans. Determinants are used in solving systems of linear equations by using Cramer's Rule. Cramer's Rule states that the solution to a system of linear equations can be found by taking the ratio of the determinants of matrices formed by replacing the coefficients of the unknown variables with the constants in each equation. This method allows for the determination of unique solutions, no solution, or infinite solutions to the system of equations.
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