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Solving a system of Linear Equations Using Inverse of a Matrix Part 2 Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

Timeline

00:03 Solving System of Linear Equations using Matrices
00:46 Inverse of a Matrix
01:01 Determinant of a Matrix
01:18 Adjoint of a Matrix
02:24 Multiplication of Matrices
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FAQs on Solving a system of Linear Equations Using Inverse of a Matrix Part 2 Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the inverse of a matrix?
Ans. The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix. It is denoted as A^-1, where A is the original matrix.
2. How can the inverse of a matrix be used to solve a system of linear equations?
Ans. To solve a system of linear equations using the inverse of a matrix, we can represent the system in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. By finding the inverse of matrix A, we can multiply both sides of the equation by A^-1 to obtain X = A^-1 * B, which gives us the solution for the variables.
3. Are all matrices invertible?
Ans. No, not all matrices are invertible. A matrix is invertible (or non-singular) if and only if its determinant is non-zero. If the determinant is zero, the matrix is singular and does not have an inverse.
4. Can the inverse of a matrix be computed for any size of the matrix?
Ans. The inverse of a matrix can be computed for square matrices only, i.e., matrices that have an equal number of rows and columns. For non-square matrices, the inverse does not exist.
5. What happens if a matrix does not have an inverse?
Ans. If a matrix does not have an inverse, it is called a singular matrix. In the context of solving a system of linear equations, this means that the system either has no solution or infinitely many solutions, depending on the specific properties of the matrix.
204 videos|288 docs|139 tests

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