Matrices Solns of System of Equations

[Karun]

for what values of a,b the system of equations has infinite solns
x+y+z=5,
x+3y+3z=9,
x+2y+az = b

Options:
1. a=2, b=7
2. a=2, b not equal to 7
3. a not equal to 2, b not equal to 7
4. a not equal to 2, b=7

I got the answer as option 1 and 2
pls help me the answer is given as option 1 only

 

[HallsofIvy]

I wouldn't use "matrices" at all.

Subtracting the first equation from the second eliminates x and gives 2y+ 2z= 4. Dividing both sides by 2, y+ z= 2, y= 2- z.

Subtracting the first equation from the third also eliminates x and gives y+ (a-1)z= b- 5.

Since y= 2- z, 2- z+ (a- 1)z= 2+ (a- 2)z= b-5.

Divide both sides by a- 2: z= (b- 5)/(a- 2).

If a is not 2, a- 2 is not 0 so there is a single solution.
If b is not 5 and a= 2, a- 2 is 0 while b-5 is not so there is no solution.
if b= 5 and a= 2, b- 5 is 0 and a- 2 is 0 so there are infinitely many solutions.

Continue

 

[Otis]

Hi Karun. Are you in a linear algebra class, working with matrices?

If you'd like help understanding why your work gave the wrong answer, then you'll need to show us what you did.

?