Write a system of linear equations represented by the augmented matrix. Then write the solution set.
1
−
2
3
−
1
0
1
4
−
11
0
0
1
−
2
Expert Solution & Answer
To determine
To calculate:The system of linear equations represented by the augmented matrix.
1−23−101411001−2
Also, write its solution set.
Answer to Problem 1RE
The system of linear equations represented by the given augmented matrix is:
x−2y+3z=−1y+4z=−11z=−2
And the solution set of the given augmented matrix is −1,−3,−2 .
Explanation of Solution
Calculation:
Consider the given augmented matrix 1−23−101411001−2 .
Now, to construct the system of linear equations represented by the given augmented matrix, the elements of the augmented matrix on the left side of the vertical bar are the coefficients of variable terms in the equation and on the right side of the vertical bar are the constant terms.
Then, the linear equations can be written as:
x−2y+3z=−10x+y+4z=−110x+0y+z=−2
Solve further as:
x−2y+3z=−1y+4z=−11z=−2
Also, solve for the solution set of the given augmented matrix as:
1−23−101411001−2
Apply operation 2R2+R1→R1 on above matrix as:
1011−2301411001−2
Apply operations -11R3+R1→R1 and -4R3+R2→R2 on above matrix as:
100−1010−3001−2
So, the solution set is −1,−3,−2 .
Therefore, the system of linear equations represented by the given augmented matrix is:
x−2y+3z=−1y+4z=−11z=−2
And the solution set of the given augmented matrix is −1,−3,−2 .
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Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
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1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
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3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
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College Algebra with Modeling & Visualization (5th Edition)
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