LINEAR ALGEBRA TEST 1 QUESTIONS
AND ANSWERS
Every elementary Row operation is reversible - Answer-true by definition
A 5 X 6 matrix has 6 rows - Answer-false (it has 5 rows)
The solution set of a linear system involving variables x1...xn is a list of numbers
(s1...sn) that makes each equation in the system a true statement when the values
s1...sn are substituted for x1...xn, resprectively - Answer-false (The description applies
to a single solution. The solution set consists of all possible solutions. Only in special
cases does the solution set consist of exactly one solution. Mark a statement True only
if the statement is always true.)
Two fundamental questions about a linear system involve existence and uniqueness -
Answer-true (Fundamental questions about a linear system definition)
In some cases, a matrix may be row reduced to more than one matrix in reduced
echelon form, using different sequences of row operations - Answer-false (Each matrix
is row equivalent to one and only one reduced echelon matrix)
The row reduction algorithm applies only to augmented matrices for a linear system -
Answer-false(By definition of of the algorithm)
a Basic variable in a linear system is a variable that corresponds to a pivot column in
the coefficient matrix - Answer-true (Definition of free variables)
Finding a parametric description of the solution set of a linear system is the save as
*solving* the system - Answer-true (Definition of Parametric Descriptions of Solution
Sets.)
If one row in an echelon form of an augmented matrix is [00050], then the associated
linear system is inconsistent - Answer-False (The row shown corresponds to the
equation 5x4 = 0, which does not by itself lead to a contradiction. So the system might
be consistent or it might be inconsistent.)
Another notation for the vector {-4 3} is [-4 3] (curly brace for vertical align) - Answer-
false (The alternative notation for a column vector is parentheses (-4, 3))
the points in the plane corresponding to {-2 5} and {-5 2} lie on a line through the origin -
Answer-false( plotting the points will verify this)
An example of a linear combination of vectors v1 and v2 is the vector 1/2v1 - Answer-
true (for example, v2*0)
AND ANSWERS
Every elementary Row operation is reversible - Answer-true by definition
A 5 X 6 matrix has 6 rows - Answer-false (it has 5 rows)
The solution set of a linear system involving variables x1...xn is a list of numbers
(s1...sn) that makes each equation in the system a true statement when the values
s1...sn are substituted for x1...xn, resprectively - Answer-false (The description applies
to a single solution. The solution set consists of all possible solutions. Only in special
cases does the solution set consist of exactly one solution. Mark a statement True only
if the statement is always true.)
Two fundamental questions about a linear system involve existence and uniqueness -
Answer-true (Fundamental questions about a linear system definition)
In some cases, a matrix may be row reduced to more than one matrix in reduced
echelon form, using different sequences of row operations - Answer-false (Each matrix
is row equivalent to one and only one reduced echelon matrix)
The row reduction algorithm applies only to augmented matrices for a linear system -
Answer-false(By definition of of the algorithm)
a Basic variable in a linear system is a variable that corresponds to a pivot column in
the coefficient matrix - Answer-true (Definition of free variables)
Finding a parametric description of the solution set of a linear system is the save as
*solving* the system - Answer-true (Definition of Parametric Descriptions of Solution
Sets.)
If one row in an echelon form of an augmented matrix is [00050], then the associated
linear system is inconsistent - Answer-False (The row shown corresponds to the
equation 5x4 = 0, which does not by itself lead to a contradiction. So the system might
be consistent or it might be inconsistent.)
Another notation for the vector {-4 3} is [-4 3] (curly brace for vertical align) - Answer-
false (The alternative notation for a column vector is parentheses (-4, 3))
the points in the plane corresponding to {-2 5} and {-5 2} lie on a line through the origin -
Answer-false( plotting the points will verify this)
An example of a linear combination of vectors v1 and v2 is the vector 1/2v1 - Answer-
true (for example, v2*0)
