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
Step-by-step explanation:
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Answer:
no statement
Step-by-step explanation:
List the statements pls
Answer: C. (10, -10)
Step-by-step explanation:
Given
1) 2x-3y=50
2) 7x+8y=-10
Multiply both sides of 1) equation by 3.5
1) 3.5(2x-3y)=3.5×50
7x-10.5y=175
2) 7x+8y=-10
Subtract 2) equation from the 1)
(7x-10.5y)-(7x+8y)=175-(-10)
-18.5y=185
y=-10
x=10
(10, -10)
Hope this helps!! :)
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