Help plsls I’ll brainlist i promise this one’s abit confusing tho.
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.
The scenario can be described using a piecewise function like:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
<h3>When the value exists but the limit does not?</h3>
Remember that the limit only exists if the limit from left and the limit from the right give the same value.
Then, we can just define a piecewise function of the form:
f(x) = 1/x if x < c.
f(x) = x if x = c
f(x) = 1/(x + 73) if x > c.
Clearly, this is not a continuous function.
Notice that:
So the limits from left and right are different, then:
Does not exist.
If you want to learn more about limits:
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