Answer:
B. Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax=0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax= 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.
Step-by-step explanation:
the answer to the question is answer B. and here is the explanation below
let us imagine that the equation ax = b has a solution
now our goal will be to show that the solution of ax =b when ax = 0 has only trivial solution.
ax = 0 is homogenous
if this equation was consistent for b, we define
ax = b to be a set of vector that has the form
w = m + gh(h is a subscript)
gh is a solution of ax = 0
from what we have above, ax=b is in the form ofw= m+gh
with
m = solution of ax=b
gh = soulution of ax=0
ax = 0 has only trivial solution
gh = 0
with gh = 0
ax=b is w=m
so ax = b is unique.
r ≈ 16 is your answer
The volume formula is 4/3 pi<span> r cubed</span>
Let Q = quarters and D = dimes
There are a total of 1202 coins, so we have to add the quarters and dimes together to get this.
Q + D = 1202
Quarters have a value of 25 cents or 0.25, dimes have a value of 10 cents or 0.10. The combination of the amount of quarters and their respective value and the amount of dimes and their respective value equate to $123.50.
0.25Q + 0.10D = 123.50
Put the two equations together. Your system of equations is:
Q + D = 1202
0.25Q + 0.10D = 123.50
Answer: 1,000,000,000,000,000,000,000,
Step-by-step explanation: