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:
Step-by-step explanation:
The answer is already there
Step-by-step explanation:
sorry but I don't get this
so sorry.
Answer:
7. 18,480 feet
10. (a.) 1.5 (b.) 150% Sorry I don't know the answers to c & d.
Step-by-step explanation:
7.
×
= 
Hope this helps!
Answer:
The total amount of money Alex spends on 5 DVD = $ 35.
Step-by-step explanation:
Total number of DVD purchased by Alex = 5
The cost of each DVD = $9
So, the total cost of purchasing 5 DVD = 5 x ( csot of 1 DVD)
= 5 x ( $ 9) = $ 45
Now , the discount if 1 DVD = $ 2
So, the total discount of 5 DVD = 5 x ( Discount on1 DVD)
= 5 x ($ 2) = $ 10
⇒ The total amount Alex spends
= Total cost of 5 DVD - Discount on 5 DVD
= $ 45 - $ 10 = $ 35
Hence, the total amount of money Alex spends on 5 DVD = $ 35.