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Mathematics
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Linear Algebra with Applications
Quiz 1: Systems of Linear Equations
Path 4
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Question 21
Essay
Identify the row operation which transforms the matrix on the left to the matrix on the right.
Question 22
Essay
Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution.
Question 23
Essay
Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution.
Question 24
Essay
Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution , if needed.
Question 25
Essay
Convert the given system to an augmented matrix, and find all solutions by transforming to reduced echelon form and using back substitution.
Question 26
Essay
Convert the given system to an augmented matrix, and find all solutions by transforming to reduced echelon form and using back substitution.
Question 27
True/False
Every homogeneous linear system has at least one solution.
Question 28
True/False
A linear system with infinitely many solutions must have more variables than equations.
Question 29
True/False
A linear system with a unique solution can not have more variables than equations.
Question 30
Essay
The volume of traffic for a collection of intersections is shown. Find all possible values for
,
,
, and
.
Question 31
Essay
The volume of traffic for a collection of intersections is shown. Find the minimum volume of traffic from C to D.
Question 32
Essay
Find all possible equilibrium and endpoint temperatures for the heavy wires with endpoints held at the indicated temperatures.
Question 33
Essay
Find the equilibrium temperatures for the heavy wires with endpoints held at the given temperatures.
Question 34
Short Answer
An economy has three industries: A, B, and C. These industries have annual consumer sales of 45, 37, and 64 (in millions of dollars), respectively. In addition, for every dollar of goods that A sells, A requires 25 cents from B and 15 cents from C. For each dollar of goods that B sells, B requires 35 cents from A and 25 cents from C. For each dollar of goods that C sells, C requires 20 cents from A and 45 cents from B. Let a, b, c be the total output from industries A, B, C, respectively. What values of a, b, c (rounded to the nearest thousand dollars) will satisfy both consumer and between-industry demand?
Question 35
Essay
Balance the given chemical equation.