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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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