Matrices

Question 1

Answer 1

Question 2

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Question 16

Answer 16

0

Question 17

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Question 18

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Question 19

What is the reduced echelon form of a matrix (after row reduction)?

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

What are linearly independent vectors?

Answer 22

Vectors for which there is no linear combination that equals 0 other than multiplying each term by 0.

Question 23

What are linearly dependent vectors?

Answer 23

Vectors for which there is some linear combination that equals 0.

Question 24

How can you determine how many vectors are linearly independent in a given set of vectors?

What is this number called?

Answer 24

Turn them into a matrix (each row is a vector) and get it into row echelon form. The number of nonzero rows is the number of linearly independent vectors (because the method of row reduction could work backwards to get the original vectors back).

This number is called the “rank” of the matrix.

Question 25

Answer 25

=rank(A)

Question 26

Answer 26

The functions are linearly independent.