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: -7 = e
Step-by-step explanation: To solve this equation for <em>e</em>, we need to get <em>e</em> by itself on the right side of the equation. Since <em>e</em> is multiplied by 16, in order to get <em>e</em> by itself, we need to divide by 16 on the right side of the equation. If we divide by 16 on the right side of the equation, we must also divide by 16 on the left side of the equation.
On the right side of the equation the 16's cancel and we have <em>e</em>. On the right side of the equation -112 divided by 16 is -7. Remember that a negative divided by a positive is a negative.
So we have -7 = e which is the solution to our equation.
To check our solution, we can plug -7 in for <em>e</em> in the original equation. So we have -112 = 16 (-7) or -112 = -112 which is a true statement so our answer checks.
Answer:
a)12 b)12 c)36
Step-by-step explanation:
a)find the least common multiple. the number of marbles is that number * n (where n is an integer)
b) the least common multiple. it is 4*3=...
c)12*3 =?
then just divide by 2,3,4 to get the answer
Answer:
15.4 (rounded to 1dp)
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
what i did is try to make some whole number and the minimum i got was 4.
1/4 = 0.25 so then do 12+4=16. then do 16*0.25=4. now do 4-6=(-2) then 1/2=0.5. now do 0.5* -2= -1. now do 4-1=3. now when there's no answer x can equal anything
