Help me solve this problem please
1 answer:
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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:
Slope = or -1
y = 6
Step-by-step explanation:
The equation given (y = 6 - x) is the same as saying
y = -1x + 6
Since we have a negative x variable and a positive 6 and would also be graphed the same. The only difference is that the second equation I just mentioned resembles the y = mx + b expression more. In this case the slope would be
Slope = or -1
While the y-intercept would be
y = 6 - x
y = 6 - 0
y = 6