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Matrices and Elementary Row Operation

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Warm-up A= B=

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Elementary Row Operations A SQUARE matrix is an elementary matrix if it is obtained from the identity matrix by a single elementary row operation. Elementary row operations: Type I: Interchange two rows. Type II: Multiply a row by a non-zero constant. Type III: Add a multiple of one row to another.

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Type I Type II Type III R3 => R1 (-)R2 (-7)R3 + R1

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Practice R2 => R1 (½)R1 (-2)R1 + R

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x-2y+3z=9 y =5 2x-5y+5z= R1+R3 2. R2+R3 3. (½)R AUGMENTED MATRIX

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SOLVE FOR X,Y,Z x=1, y=-1, z=2 Using back-substitution

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Elementary Row Operation x+y+z=6 2x -y +z=3 3x-z= x=1, y=2, z=3

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2x-y+3z=24 2y -z=14 7x-5y=6 x+2y-3z=-28 4y +2z=0 -x+y-z=-5 x=8, y=10, z=6 x=-4, y=-3, z=6

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