# Using matrices to solve systems of linear equations.

• Nov 14th 2011, 09:56 AM
Lotte1990
Using matrices to solve systems of linear equations.
Hello,

Could someone please tell me how to solve exercises 11, 22 and 26?

Exercise 11
The answer of exercise 11 should be that b is not a linear combination of a1, a2 and a3. I computed the echelon form of the augmented matrix where a1, a2, a3 and b are the columns of the augmented matrix, but I end up with a consistent system, so I don't understand why b is not a linear combination of a1, a2 and a3.

Exercise 22
Not even a clue where to start...???

Exercise 26
In 26(a) I found that the system is consistent, so b is in W. How do I solve 26(b)?

Lotte
• Nov 14th 2011, 10:31 AM
Deveno
Re: Linear Algebra Help!
when i reduce the augmented matrix in #11, i get:

$\begin{bmatrix}1&0&5&2\\0&1&4&3\\0&0&0&-15\end{bmatrix}$

the last row implies $0a_1 + 0a_2 + 0a_3 = 0 = -15$

doesn't look consistent to me.
• Nov 14th 2011, 10:57 AM
Lotte1990
Re: Linear Algebra Help!
Where did I go wrong?

$\begin{bmatrix}1&0&5&2\\-2&1&-6&-1\\0&2&8&6\end{bmatrix}$

(Add 2 times the 1st row to the 2nd row)

$\begin{bmatrix}1&0&5&2\\0&1&4&3\\0&2&8&6\end{bmatr ix}$

(Add -2 times the 2nd row to the 3rd row)

$\begin{bmatrix}1&0&5&2\\0&1&4&3\\0&0&0&0\end{bmatr ix}$

• Nov 15th 2011, 04:01 AM
Lotte1990
Re: Linear Algebra Help!
I used MATLAB to get the row reduced echelon form of this matrix. MATLAB gives the same row reduced echelon form I found.
Does anyone know how Deveno ended up with an inconsistent row? The answer of exercise 11 should be that b is not a linear combination of a1, a2 and a3.
I don't understand why, because the row reduced echelon form of the matrix shows a consistent system...