Answer:
True
True
False
Step-by-step explanation:
TRUE
If the equation Ax = 0 has only the trivial solution, then A is row equivalent to the n × n identity matrix
Here's why
If the equation Ax = 0 has only the trivial solution the determinant of the matrix is NOT 0 and the matrix is invertible therefore it is row equivalent to the nxn identity matrix.
TRUE
If the columns of A span ℝ^n , then the columns are linearly independent
Here's why
Remember that the rank nullity theorem states that
According to the information given we know that
Therefore you have
and
Which is equivalent to the problem we just solved.
FALSE
If A is an n × n matrix, then the equation Ax = b has at least one solution for each b in ℝ^n
Here's why
Take b as a non null vector and A=0, then Ax = 0 and Ax=b will have no solution.
The correct answer is G. y=15x+80 because y represents the total, 15x represents the number of months times 15 because it increases by 15 members every month. And then you started with 80, so there's plus 80 at the end.
Answer:
A. $,143,699,010
Step-by-step explanation:
Use a calculator my friend.
True. If they never intersect then they must have the same slope and are parallel