Question

True or False

a. The equation Ax=b is referred to as a vector equation.
b. 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.

c. The equation Ax=b is consistent if the augmented matrix [ A b] has a pivot position in every row.

d. The first entry in the product Ax is a sum of the products.

e. If the colums of an mxn matrix of A span R^m , then the equation Ax=b is consistent for each b in R^m.

f. If A is an mxn matric and if the equation Ax=b is inconsistent for some b in R^m, then A cannot have a pivot p

Answer 1

last part of f is position in every row.

Answer 2

so a. is true

Answer 3

help me please!

Answer 4

So answer to a. is False- It's referred to a matrix equation

Answer to b. is True-The equation Ax=b has a solution if and only if b is a linear combination of the colum ns of A.

Answer 5

c. is Fasle-If an augmented matrix [A b] has a pivit posititon in every row, then the equation Ax=b may or may not be consistent.

Answer 6

i need help with e and f

Answer 7

I think e is true, but I don't know why and I think f is true, but don't know why

Answer 8

what does 'being consistent' mean? Did you define that in class as a mathematical term of solutions sets for linear equations? I haven't read that word before in linear algebra.

Answer 9

A system of linear equations is said to be consistent if it has either one solution or infinite solutions

Answer 10

I think i got e. figured out

Answer 11

e is true because spanning R^m means every vector in R^m can be written as a linear combination of the vectors take make up the column of A.

Recall the fact that there must be at least m linear independent vectors to span R^m. Because the matrix mxn span R^m we know there are at least m linearly independent vectros

Answer 12

okay

Answer 13

how about f?

Answer 14

I forgot what is pivot point is lol

Answer 15

pivot positions is where you have to either have a -1 or 1 at every entry