Question

1. a) How many solutions exist for the system of equations x + 2y – 3z = 4, x + 3y + z = 11, 2x + 5y - 4z = 13, and 2x + 6y + 2z = 22. Find all those solutions. ​

Answer 1

Answer:

Solution

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Correct option is

A

there is only one solution

Given,

x+2y+3z=1

2x+y+3z=2

5x+5y+9z=4

we have,

determinant,

∣A∣=

∣

∣

∣

∣

∣

∣

∣

∣

1

2

5

2

1

5

3

3

9

∣

∣

∣

∣

∣

∣

∣

∣

∣A∣=1(9−15)−2(18−15)+3(10−5)

∣A∣=−6−6+15

∣A∣=3

∣A∣



=0

∣A∣= determinant of coefficient matrix



=0

Therefore there exists a unique solution ( only one solution)

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