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Answer:
The reduced row-echelon form is
The solutions to the system of equations are:
Step-by-step explanation:
To solve this system of linear equations,
you must:
Step 1: Transform the augmented matrix to the reduced row echelon form.
In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.
This is the augmented matrix that represents the system.
It can be transformed by a sequence of elementary row operations to the matrix.
There are three kinds of elementary matrix operations.
- Interchange two rows (or columns).
- Multiply each element in a row (or column) by a non-zero number.
- Multiply a row (or column) by a non-zero number and add the result to another row (or column).
Using elementary matrix operations, we get that
Row Operation 1: add -2 times the 1st row to the 2nd row
Row Operation 2: add 1 times the 1st row to the 3rd row
Row Operation 3: multiply the 2nd row by -1/3
Row Operation 4: add -2 times the 2nd row to the 3rd row
Row Operation 5: add 4 times the 2nd row to the 1st row
Step 2: Interpret the reduced row echelon form
The reduced row echelon form of the augmented matrix is
which corresponds to the system
The system has infinitely many solutions.
Answer:
<u>The function f(x)=a(x-h)² + k is the parabola with vertex:</u>
- (h, k)
If the vertex is in the second quadrant, the h < 0 and k > 0
It can open up or down, so a ≠0, it opens up if a > 0, opens down if a < 0
The axis of symmetry is the line parallel to y-axis and passing through the vertex, so it would be the line:
- x = h
<u>Now let's assume h = -5, k = 2, a = 1, then our function is:</u>
- f(x) = (x + 5)² + 2
The graph is attached and it opens up as a = 1 > 0
<u>The line of symmetry is </u>
- x = - 5
