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Important Matrices Formulas for JEE and NEET
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FAQs on Important Matrices Formulas for JEE and NEET
| 1. What are the basic operations that can be performed on matrices? |  |
Ans. The basic operations that can be performed on matrices include addition, subtraction, and multiplication. In addition and subtraction, matrices of the same dimensions can be combined element-wise. For multiplication, a matrix can be multiplied by another matrix if the number of columns in the first matrix equals the number of rows in the second matrix.
| 2. How do you calculate the determinant of a matrix? | |
Ans. The determinant of a matrix can be calculated using various methods depending on the size of the matrix. For a 2x2 matrix, the determinant is calculated as ad - bc, where the matrix is represented as [[a, b], [c, d]]. For larger matrices, methods such as expansion by minors or row reduction can be used.
| 3. What is the inverse of a matrix and how is it calculated? | |
Ans. The inverse of a matrix A, denoted as A^(-1), is a matrix such that when multiplied by A, yields the identity matrix. A matrix has an inverse only if its determinant is non-zero. To calculate the inverse, one can use the formula A^(-1) = (1/det(A)) * adj(A), where adj(A) is the adjugate of A.
| 4. What is the difference between a row matrix and a column matrix? | |
Ans. A row matrix is a matrix with only one row and multiple columns, represented as a 1 x n matrix. In contrast, a column matrix has only one column and multiple rows, represented as an m x 1 matrix. The distinction is important in matrix operations, especially in multiplication and transformations.
| 5. How do you find the eigenvalues of a matrix? | |
Ans. To find the eigenvalues of a matrix A, one must solve the characteristic equation det(A - λI) = 0, where λ represents the eigenvalue and I is the identity matrix of the same dimension as A. The solutions for λ are the eigenvalues of the matrix.
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