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Vikentia [17]
2 years ago
12

Solve The Equation By Cramer's Rule:

Mathematics
2 answers:
lord [1]2 years ago
5 0
Thx for the points, have a nice dayyy
Anna11 [10]2 years ago
3 0

Answer:

Question:

x+y+z=3; x-y+z=1; x+y-2z=0

Step-by-step explanation:

-----» Given equation can be written as..

(1)x +(1)y+ (1)z =3

(1)x- (1)y+ (1)z =1

(1)x+ (1)y- (2)z =0

Step 1: We have To calculate D

\:  \:  \:  \:  \:  \:  \:  \:  \:  |1 \:   \:  \:  \: 1 \:  \: \:  \:  \:  1 \:  \: | \\  d \:  = |1 \:  - 1 \:  \:  \:  \:  \: 1|  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  |1 \ \:  \:    1 \:  \:  \:  - 2|

=1[(-1)(-2)-(1)(1)]-1[(1)(-2)-(1)(1)]+1[(1)(1)-(-1)(1)]

=1[2-1] -1[-2-1] +1[1+1]

=1(1) -1(-3) +1(2)

=1+3+2

<h3><u>D=</u><u>6</u></h3>

______________________________________

Step 2: We have to calculate Dx!!

\:  \:  \:   \:  \:  \:  \:  \:  \:  \:  \:  \: \:   \:  |3 \:  \:  \:  \:  \: 1   \:  \:  \:  \:  \: \:  1| \\ DX=|1\:  \:  - 1  \:  \: \: 1 | \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: |0 \:  \: 1 \:  \:  - 2|

=3[(-1)(-2)-(1)(1)] -1[(1)(-2)-(1)(0)]+1[(1)(1)-(-1)(0)]

=3(2-1) -1(-2-0) +1(1-0)

=3(1) -1(-2) +1(1)

=3+2+1

<h3><u>DX=</u><u>6</u></h3>

<u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u>

Step 3: We have to calculate Dy!

\:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  |1 \:   \:  \:  \: 3 \:  \: \:  \:  \:  \:  1| \\dy= |1 \:   \:  \:  \:  \:  1 \:  \:  \:  \:  \: 1|  \\  \:  \:  \:  \:  \:  \:  \:   \:  \: \:  \:  \: \:     \: |1 \:  \:  \: \:  \: 0 \:   \:  - 2|

=1[(1)(-2)-(1)(0)]-3[(1)(-2)-(1)(1)]+1[(1)(0)-(1)(1)]

=1(-2-0)-3(-2-1)1(0-1)

=1(-2)-3(-3)1(-1)

= -2+ 9- 1

<h3><u>Dy=</u><u>6</u></h3>

______________________________________

Step4: we have to calculate Dz!!

\:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  |1 \:   \:  \:  \: 1 \:  \: \:  \:  \:  \:  \: 3| \\  d \:  = |1  \:  - 1 \:  \:  \:  1|  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  | \:  \: 1 \ \:  \:    1 \:   \:  \: \:  \: \:   0|

=1[(-1)(0)-(1)(1)] -1[(1)(0)-(1)(1)] +3[(1)(1)-(-1)(1)]

=1(0-1) -1(0-1) +3(1+1)

=1(-1)-1(-1)3(2)

=-1+1+6

<h3><u>Dz=</u><u>6</u></h3>

______________________________________

Now, By Cramer's Rule~~

x  = \frac{dx}{x} =  \frac{6}{6} = 1

y = \frac{dy}{y} =  \frac{6}{6} = 1

z =  \frac{dz}{z} =  \frac{6}{6} = 1

<h3><u>x=</u><u>1</u><u> </u><u> </u><u>y=</u><u>1</u><u> </u><u> </u><u>z</u><u>=</u><u>1</u>!!</h3>

Hope it helps!!

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