Matrices and Determinants

addition, substruction, multiplication, Referat, Hausaufgabe, Matrices and Determinants
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Today we are going to talk about Matrices and Determinants . I will explain you two different ways of solving an equation system by using matrices and how to do simple calculations like multiplication and addition with matrices. If we have an equation system like this: 1x 1y-1z 6 3x-1y 3z 11 4x 2y-3z 14 we can solve it by using the two methods we learned to solve linear equation systems with two unknown variables but this would be very difficult. An idea to simplify the system would be to write only the numbers and to leave out the variables. We get a matrix with 3 rows and 4 columns: 1 1 -1 6 2 -1 3 11 4 2 -3 14 It is a rule, that you can add any row multiplied with any number to any other row without changing the matrix worth, so we add -2 multiplied with the middle row to the last row. The aim of this operation is, to get a zero in the column representing the x. 1 1 -1 6 2 -1 3 11 0 4 -9 -8 Our next operation is, to add -2 multiplied by the 1st row to the middle row, leaving the middle row with a zero in the first column. 1 1 -1 6 0 -3 5 -1 0 4 -9 -8 Finally, we add 4 3 multiplied by the middle row to the bottom row and so we have finished the so-called triangulariztion process. We get the matrix 1 1 -1 6 0 -3 5 -1 0 0 -21 3 -91 3 Now we can fill in the x s y s and z s again, and we see that the equation system is nearly solved: 1x 1y -1z 6 -3y 5z -1 -21 3z -91 3 Now we can easily solve the equation system..................we get the result: z 4; y 7; x 3 Matrices are ...

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