LINEAR ALGEBRA EXAM TRUE/FALSE
QUESTIONS AND ANSWERS
Two matrices are row equivalent if they have the same number of rows - Answer-False
Elementary row operations on an augmented matrix never change the solution set of
the associated linear system - Answer-True
Two equivalent linear systems can have different solution sets - Answer-False
A consistent system of linear equations has one or more solutions - Answer-True
Suppose a 3x6 coefficient matrix for a system has three pivot columns. Is the system
consistent? Why or why not? - Answer-There is a pivot in each row, so the system is
consistent.
Another notation for the vector
[-4]
[3]
is [-4 3] - Answer-False (-4, 3)
The points in the plane corresponding to (-2,5) and (-5,2) lie on a line through the origin.
- Answer-False
An example of a linear combination of vectors v1 and v2 is the vector 1/2(v1) - Answer-
True
The solution set of the linear system whose augmented matrix is [a1 a2 a3 b] is the
same as the solution set of the equation x1a1 + x2a2 + x3a3 = b. - Answer-True
The set Span {u, v} is always visualized as a plane through the origin. - Answer-False
The equation Ax=b is referred to as a vector equation - Answer-False
A vector b is a linear combination of the columns of a matrix A if and only if the equation
Ax=b has at least one solution. - Answer-True
The equation Ax=b is consistent if the augmented matrix [A b] has a pivot position in
every row. - Answer-False
The first entry in the product Ax is a sum of products - Answer-True
If the columns of an mxn matrix A span Rm, then the equation Ax=b is consistent for
each b in Rm. - Answer-True
QUESTIONS AND ANSWERS
Two matrices are row equivalent if they have the same number of rows - Answer-False
Elementary row operations on an augmented matrix never change the solution set of
the associated linear system - Answer-True
Two equivalent linear systems can have different solution sets - Answer-False
A consistent system of linear equations has one or more solutions - Answer-True
Suppose a 3x6 coefficient matrix for a system has three pivot columns. Is the system
consistent? Why or why not? - Answer-There is a pivot in each row, so the system is
consistent.
Another notation for the vector
[-4]
[3]
is [-4 3] - Answer-False (-4, 3)
The points in the plane corresponding to (-2,5) and (-5,2) lie on a line through the origin.
- Answer-False
An example of a linear combination of vectors v1 and v2 is the vector 1/2(v1) - Answer-
True
The solution set of the linear system whose augmented matrix is [a1 a2 a3 b] is the
same as the solution set of the equation x1a1 + x2a2 + x3a3 = b. - Answer-True
The set Span {u, v} is always visualized as a plane through the origin. - Answer-False
The equation Ax=b is referred to as a vector equation - Answer-False
A vector b is a linear combination of the columns of a matrix A if and only if the equation
Ax=b has at least one solution. - Answer-True
The equation Ax=b is consistent if the augmented matrix [A b] has a pivot position in
every row. - Answer-False
The first entry in the product Ax is a sum of products - Answer-True
If the columns of an mxn matrix A span Rm, then the equation Ax=b is consistent for
each b in Rm. - Answer-True
