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3 years ago

Solve the following system of equations using matrices (row operations).

Mathematics

1 answer:

Stells [14]3 years ago

6 0

Answer:

(6,3,0)

Step-by-step explanation:

Given,

x - y + 0z = 3

6x - 0y - 2z = 36

0x + 6y + 2z = 18

You have the following augmented matrix:

(1) 1 -1 0 3

(2) 6 0 -2 36

(3) 0 6 2 18

Let's (3) add to (2) and divide by 6

(1) 1 -1 0 3

(2) 1 1 0 9

(3) 0 6 2 18

Now, let's (2) add to (1) and divide by 2

(1) 1 0 0 6

(2) 1 1 0 9

(3) 0 6 2 18

Let's (3) ÷ 2

(1) 1 0 0 6

(2) 1 1 0 9

(3) 0 3 1 9

Let's (1) subtract from (2)

(1) 1 0 0 6

(2) 0 1 0 3

(3) 0 3 1 9

Finally, let's (2) multiply by 3 and subtract from (3)

(1) 1 0 0 6

(2) 0 1 0 3

(3) 0 0 1 0

Thus,

x = 6, y = 3 and z = 0

The answer is (6, 3, 0)

We have to verify the answer

6 - 3 = 3 ⇒⇒ 3 = 3

6*6 - 5*0 = 36 ⇒⇒ 36 = 36

6*3 + 2*0 = 18 ⇒⇒ 18 = 18

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Solve the following system of equations using matrices​ (row operations).

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