Looneytunness2875 Looneytunness2875
  • 01-07-2021
  • Mathematics
contestada

Suppose Ax = b always has at least one solution no matter what b is. Why AT y = 0 has only the trivial solution y = 0?

Respuesta :

facundo3141592
facundo3141592 facundo3141592
  • 04-07-2021

Answer:

For the first equation we have:

A*x = b

solving for x, we get:

x = b/A

If it always has a solution, then we can not have A = 0, because that causes an undefined operation.

so for example, if we have A = 1 and b = 2

x = b/A = 2/1

For the other case,

A*y = 0

dividing both sides by A

y = 0/A = 0

y = 0

Here we have only one possible solution, the trivial one, y = 0.

And the dependence on A disappears (because the quotient between zero and a number different than zero is always zero)

Answer Link

Otras preguntas

(10y^3+20y^2+55y)/5y
Can someone use the word delta in a sentence
what is the answer for (20,8),(9,16) ?
Which equation has the same y-intercept as y=4x-3?a. y-3=x              b. y=8x+3    c. 3-y=4x      d. y=-3+8xWhich of the following is the equation of the line
How is it possible for Mercury to have frozen ice ?
Data are drawn from a symmetric and bell shaped distribution with a mean of 120 and a standard deviation of 5. There are 900 observations in the data set. What
Historians of china have traditionally dated the beginning of Chinese civilization to the founding of the what??
Can someone use the word delta in a sentence
Data are drawn from a symmetric and bell shaped distribution with a mean of 120 and a standard deviation of 5. There are 900 observations in the data set. What
find an equivalent expression without parentheses -(50x-15y+15)=