Assignment
Linear Algebra M240 True-False
-
University:
Whitman College -
Course:
MATH-240 | Linear Algebra Academic year:
2022
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Views:
424
Pages:
17
Author:
hernomenvxp
1.1.23
1
Every elementary row operation is reversible.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
2
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
A 5 × 6 matrix has six rows.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
2
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
A 5 × 6 matrix has six rows.
False. The matrix has 5 rows, 6 columns.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
2
A 5 × 6 matrix has six rows.
False. The matrix has 5 rows, 6 columns.
3
The solution set is a list of numbers that makes each equation in the
system a true statement.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
2
A 5 × 6 matrix has six rows.
False. The matrix has 5 rows, 6 columns.
3
The solution set is a list of numbers that makes each equation in the
system a true statement.
False.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
2
A 5 × 6 matrix has six rows.
False. The matrix has 5 rows, 6 columns.
3
The solution set is a list of numbers that makes each equation in the
system a true statement.
False. The solution set is the set of all such lists of numbers that
makes each equation in the system a true statement.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
2
A 5 × 6 matrix has six rows.
False. The matrix has 5 rows, 6 columns.
3
The solution set is a list of numbers that makes each equation in the
system a true statement.
False. The solution set is the set of all such lists of numbers that
makes each equation in the system a true statement.
4
Two fundamental questions about a linear system involve existence
and uniqueness.
January 19, 2017
1/2 1.1.23
1
Every elementary row operation is reversible.
True.
I
I
I
If rj ← crj , then rj ← c1 rj is inverse.
If rj ↔ ri , then swap them back to invert.
Given rk ← rk + Crj , then rk ← rk − Crj would invert.
2
A 5 × 6 matrix has six rows.
False. The matrix has 5 rows, 6 columns.
3
The solution set is a list of numbers that makes each equation in the
system a true statement.
False. The solution set is the set of all such lists of numbers that
makes each equation in the system a true statement.
4
Two fundamental questions about a linear system involve existence
and uniqueness.
True. See pg. 8.
January 19, 2017
1/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
2
Elementary row operations on an augmented matrix never change the
solution set of the associated linear system.
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
2
Elementary row operations on an augmented matrix never change the
solution set of the associated linear system.
True. (That’s why we use these particular row ops)
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
2
Elementary row operations on an augmented matrix never change the
solution set of the associated linear system.
True. (That’s why we use these particular row ops)
3
Two equivalent linear systems can have different solution sets.
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
2
Elementary row operations on an augmented matrix never change the
solution set of the associated linear system.
True. (That’s why we use these particular row ops)
3
Two equivalent linear systems can have different solution sets.
False. To be equivalent, the linear systems must have the same
solution set.
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
2
Elementary row operations on an augmented matrix never change the
solution set of the associated linear system.
True. (That’s why we use these particular row ops)
3
Two equivalent linear systems can have different solution sets.
False. To be equivalent, the linear systems must have the same
solution set.
4
A consistent system of linear equations has one or more solutions.
January 19, 2017
2/2 1.1.24
1
Two matrices are row equivalent if they have the same number of
rows.
False. Row equivalence means that we can convert one matrix to the
other using elementary row operations.
2
Elementary row operations on an augmented matrix never change the
solution set of the associated linear system.
True. (That’s why we use these particular row ops)
3
Two equivalent linear systems can have different solution sets.
False. To be equivalent, the linear systems must have the same
solution set.
4
A consistent system of linear equations has one or more solutions.
True. This is the definition of a consistent system.
January 19, 2017
2/2
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