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Test 3 Study Guide - Test 3 Study Guide Objectives...

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Test 3 Study Guide Objectives: Implement the row reduction algorithm to solve linear systems, and parameterize their solutions Find the rank and kernel of a matrix Find the inverse of an invertible matrix Find the LU Factorization of a matrix Find the image of a matrix Multiplication Inner dimensions must match Outer dimensions are dimensions for the solution matrix Multiply the first input in row one with the first input in column one, then continue across the first row and down the first column. The sum of each input results in the input for row one column one of the solution matrix. Inverses The inverse of a matrix is a special case and given by the following algorithm: For any other sized matrix, the inverse can be found by augmenting the original matrix with the identity matrix. Row operations can then be applied until the identity matrix forms on the left.
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Dot Product The dot product of two vectors results in a scalar The corresponding values are multiplied and the resulting numbers are summed to form the dot product of two vectors.
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