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6.1_bzca5e

# 6.1_bzca5e - Section 6.1 Matrix Solutions to Linear Systems...

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Section 6.1 Matrix Solutions to Linear Systems

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Solving Linear Systems Using Matrices
This rectangular array of 24 numbers, arranged in rows and columns and placed in red brackets, is an example of a matrix. The numbers inside the brackets are called elements of the matrix. Matrices are used to solve systems of linear equations. They give us a shortened way of writing a system of equations. The first step in solving a system of linear equations using matrices is to write the augmented matrix. An augmented matrix has a vertical bar separating the columns of the matrix into two groups. The coefficients of each variable are placed to the left of the vertical line and the constants are placed to the right. If any variable is missing, its coefficient is 0.

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Notice how the second matrix contains 1s down the diagonal from upper left to lower right, called the main diagonal, and 0s below the 1s. This arrangement makes it easy to find the solution of the system of equations with just a little back-substitution.
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