Solve the following system of equations using matrices​ (row operations). x-y=3 6x-5z=36 6y+2z=18

Question

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

x-y=3
6x-5z=36
6y+2z=18

in progress 0
Thu Cúc 5 months 2021-08-22T07:28:34+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-08-22T07:29:48+00:00

    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  

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )