Matrix equation problem

[SilverKing]

Hi

I have the following matrix, and I suppose that it can be solved using Gauss' method

1 2 3
4 5 6
7 8 a^2-5



any help?

 

[Quaid]

Matrix equation problem

1 2 3
4 5 6
7 8 a^2-5

Hello. This is not an equation. Without additional information, there is nothing to solve.

Please check your typing, or repost the entire exercise -- including the instructions. Thank you. :cool:

 

[SilverKing]

Sorry for being late

y+y-z=2
x+2y+z=3
x+y+(a^2-5)z=a

Find the the values of "a" for these equations in three cases:
1. One solution
2. Infinitely number of solutions
3. No solution at all

 

[stapel]

y+y-z=2
x+2y+z=3
x+y+(a^2-5)z=a

Find the the values of "a" for these equations in three cases:
1. One solution
2. Infinitely number of solutions
3. No solution at all

I will guess that the first equation is meant to start with an "x".

To start, simplify the system, using row operations. For instance, subtract one of row one (R1) from each of the other two rows. This leaves you with:

. . . . .x + y - z = 2
. . . . .y + 2z = 1
. . . . .(a^2 - 5)z + z = a - 2

The last row simplifies as:

. . . . .(a^2 - 5 + 1)z = a - 2
. . . . .(a^2 - 4)z = a - 2

So now the system is:

. . . . .x + y - z = 2
. . . . .y + 2z = 1
. . . . .(a^2 - 4)z = a - 2

Now subtract R2 from R1, etc, until you get a completely simplified system. Then think about what it means, in terms of the forms of solutions, to get answers of each of the listed types. Use this to set up and solve equations that answer each of the questions.