Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
. - There is an n×n matrix D such that AD=.
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix .
- For each column vector b in
, the equation Ax=b has a unique solution. - The columns of A span .
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix .
The correct option is C.
Answer:
36 , 0, 79
Step-by-step explanation:
Answer:
Step-by-step explanation:
If apricots is x, and each apricot weighs 5 grams, then the expression for that is 5x; if each cherry, y, weighs 2 grams, then the expression for that is 2y. If the mix Roy wants to make needs AT LEAST 230 grams of fruit, then
5x + 2y ≥ 230 where the inequality sign "greater than or equal to" satisfies the expression "at least".
Answer:
When the number of sessions is equal to 10, the total cost is the same in the two plans
Step-by-step explanation:
Let
y ---> the total cost
x ---> the number of sessions
we know that
The linear equation in slope intercept form is equal to
where
m is the slope
b is the y-intercept
Planet Fitness
we have
The slope is equal to
The y-intercept or initial value is equal to
substitute
----> equation A
Gold's Gym
we have
The slope is equal to
The y-intercept or initial value is equal to
substitute
----> equation B
Equate equation A and equation B
solve for x
therefore
When the number of sessions is equal to 10, the total cost is the same in the two plans
<span>THE AREA OF THE ROOM IS :A=4*2.4=9.6 m^2
THICKNESS t=0.30 m
DIFFERENCE IN TEMPERATURE dT=18-6=12
q=kAdT/dx=kA*dT/t
q=1.3(9.6)(12)/0.30=4992 W=499.2 J/s
In 1 hour or 3600 sec
P=q*T=(499.2 J/s)(3600 s)=1797120 J=1.8 MJ
1.8MJ OF HEAT FLOWS HTROUGH THE WALL IN ONE HOUR</span>
