Someone Help me solve these by substitution please !
1 answer:
You might be interested in
Answer:
20x = 55
Step-by-step explanation:
First you have to add 3x to both sides of 11-3x=x
Now that you have 11 = 4x you divide 4 on both sides
11/4 = x
But you can't divide 11 by 4 unless you are looking for the decimal form of 11/4 which is 2.75
so now we take 11/4 or 2.75 depending on if you need your answer in fraction or as a decimal and replace that with x however both will equal the number 55
The vectors in form a basis of
if they are mutually linearly independent and span
.
To check for independence, we can compute the Wronskian determinant:
The determinant is non-zero, so the vectors are indeed independent.
To check if they span , you need to show that any vector in
can be expressed as a linear combination of the vectors in
. We can write an arbitrary vector in
as
Then we need to show that there is always some choice of scalars such that
This is equivalent to solving
or the system (in matrix form)
This has a solution if the coefficient matrix on the left is invertible. It is, because
(that is, the coefficient matrix is not singular, so an inverse exists)
Compute the inverse any way you like; you should get
Then
A solution exists for any choice of , so the vectors in
indeed span
.
The vectors in are independent and span
, so
forms a basis of
.