- #1

- 135

- 1

solve eqautions using a matrix

x + y -z = 0

3x - y + z = 4

5x +z = 7

so i wrote the matrix

1 1 -1 0

3 -1 1 4

5 0 1 7

then i multiplied Row 1 by -3 and added that to row 2

and multiplied row 1 by -5 and added that to row 3

resulting in

1 1 -1 0

0 -4 4 4

0 -5 6 7

then i multiplied row 2 by - 1/4

1 1 -1 0

0 1 -1 -1

0 -5 6 7

then multiplied row 2 by 5 and added that to row 3

1 1 -1 0

0 1 -1 -1

0 0 1 2

now i subbed back in to eqns

x + y -z = 0

3x - y + z = 4

5x +z = 7

1x + 1y - 1z = 0

0x +1y - 1z = -1

0x + 0y + 1z = 2

so z = 2 and solving all the other equation i get x = 1 and y = 1

is this right because i tried solving these by subtraction and got somthing different

x + y -z = 0

3x - y + z = 4

5x +z = 7

so i wrote the matrix

1 1 -1 0

3 -1 1 4

5 0 1 7

then i multiplied Row 1 by -3 and added that to row 2

and multiplied row 1 by -5 and added that to row 3

resulting in

1 1 -1 0

0 -4 4 4

0 -5 6 7

then i multiplied row 2 by - 1/4

1 1 -1 0

0 1 -1 -1

0 -5 6 7

then multiplied row 2 by 5 and added that to row 3

1 1 -1 0

0 1 -1 -1

0 0 1 2

now i subbed back in to eqns

x + y -z = 0

3x - y + z = 4

5x +z = 7

1x + 1y - 1z = 0

0x +1y - 1z = -1

0x + 0y + 1z = 2

so z = 2 and solving all the other equation i get x = 1 and y = 1

is this right because i tried solving these by subtraction and got somthing different

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