Elementary row operations

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Vectors are written as rows in these questions. R^n is the real vector space with n coordinates. Rows of a matrix are separated by semicolons. Enter your answer as concisely as possible.

Let A=[1 2 3; 2 3 4; 3 4 5]. Is A injective?

1 point

True

False

Clear selection

Let A=[1 2 3; 2 3 4; 3 4 5]. Is A surjective?

1 point

True

False

Clear selection

Let A=[1 2 3 4; 1 -2 -4 5; 2 6 7 2; 3 -5 4 5]. Is A invertible?

2 points

True

False

Clear selection

Let A=[1 2 3 4; 2 3 4 5; 3 4 5 6; 4 5 6 7]. Let b=(10,25,40,55). Ax = b has

2 points

No solution

Unique solution

Infinitely many solutions

Clear selection

Let A=[1 2 3 4; 2 3 4 5; 3 4 5 6; 4 5 6 7]. Let b=(20,25,40,55). Ax = b has

2 points

No solution

Unique solution

Infinitely many solutions

Clear selection

Let A=[1 2 3; 2 3 4; 3 4 4; 4 5 6]. Let b=(10,25,40,55). Ax = b has

2 points

No solution

Unique solution

Infinitely many solutions

Clear selection

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