F(x)=x^2-3 domain and range
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:
Step-by-step explanation:
<h3>to understand this</h3><h3>you need to know about:</h3>- conic sections
- PEMDAS
- vertices of hyperbola:(±a,0) and (0,±b) if reversed
- vertices: (0,±10)
- the hyperbola equation is inversed since the vertices is (0,±10)
- asymptotes:
- the asymptotes are in simplest and we know b is ±10
according to the question
therefore we got
- a=12
- b=10
note: the equation will be inversed
let's create the equation:
