Which matrix operation is used to solve a system of linear equations? a. Addition b. Subtraction c. Multiplication d. Inversion
Question
Which matrix operation is used to solve a system of linear equations?
a. Addition
b. Subtraction
c. Multiplication
d. Inversion
Solution
The matrix operation used to solve a system of linear equations is d. Inversion.
Here's a step-by-step explanation:
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Convert the system of linear equations into a matrix form, Ax = b, where A is the matrix of coefficients, x is the column vector of variables, and b is the column vector of solutions.
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Calculate the inverse of matrix A, denoted as A^-1. This is possible only if A is a square matrix and its determinant is not zero.
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Multiply the inverse of matrix A with the solution vector b to get the variable vector x, i.e., x = A^-1 * b. This gives the solution to the system of linear equations.
Please note that not all systems of linear equations have a unique solution or any solution at all. The existence and uniqueness of the solution depend on the properties of matrix A.
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