6 2 6
Let u = 4 , v = 2 , w = 2
5 3 1
Show that 2u - 3v - w = 0. Use that fact to find x1 and x2 that satisfy the equation
6 2 6
4 2 {x1} = 2
5 3 {x2} 1
Except that indeed 8 - 6 - 2 = 0
I have no idea what you mean.
Are x1 and x2 vectors multiplied by square matrices or what?
u=6
4
5
v=2
2
3
w=6
2
1
show that 2u - 3v - w = 0
Sorry!! I hope this makes a bit more sense...Can we try to do this step by step so I can understand it better?
Then after this, use that fact to find x1 and x2 that satisfies the equation:
6 2 6
4 2 2
5 3 {x1 and x2} = 1
just add them up:
2u-3v-w =
12-6-6
8-6-2
10-9-1
=
0
0
0
The 6
2
1
is supposed to be on the right hand side of the equal sign. I am so sorry again!!!
To show that 2u - 3v - w = 0, we substitute the given values of u, v, and w into the equation:
2u - 3v - w = 2(4) - 3(2) - 2 = 8 - 6 - 2 = 0
Therefore, we have shown that 2u - 3v - w = 0.
Now, to find x1 and x2 that satisfy the equation 6x1 + 2x2 = 6 and 4x1 + 2x2 = 2, we can use the following steps:
1. Express the given equations as a matrix equation in the form Ax = B, where A is the coefficient matrix, x is the column vector of variables, and B is the column vector of constants.
[6 2] [x1] [6]
[4 2] * [x2] = [2]
2. Rewrite the matrix equation as a system of linear equations:
6x1 + 2x2 = 6
4x1 + 2x2 = 2
3. Solve the system of equations using elimination or substitution method. In this case, we'll use the elimination method.
Multiply the first equation by 2 to obtain:
12x1 + 4x2 = 12
Subtract the second equation from the first:
(12x1 + 4x2) - (4x1 + 2x2) = 12 - 2
Simplify:
8x1 + 2x2 = 10
4. Now, we have a new system of equations:
8x1 + 2x2 = 10
4x1 + 2x2 = 2
5. Solve this new system of equations using elimination or substitution method. Again, we'll use the elimination method.
Multiply the second equation by 2 to obtain:
8x1 + 4x2 = 4
Subtract the second equation from the first:
(8x1 + 4x2) - (8x1 + 2x2) = 10 - 4
Simplify:
2x2 = 6
6. Solve for x2:
x2 = 6/2 = 3
7. Substitute the value of x2 back into one of the original equations to solve for x1. Let's use the first equation:
6x1 + 2(3) = 6
Simplify:
6x1 + 6 = 6
Subtract 6 from both sides:
6x1 = 0
Divide both sides by 6:
x1 = 0/6 = 0
Therefore, the values x1 = 0 and x2 = 3 satisfy the equation 6x1 + 2x2 = 6 and 4x1 + 2x2 = 2.