Use the Zero Product Property to find the x-intercepts for x^2+6x=y
1 answer:
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For the most part, the cross-section formed is a <em>trapezoid</em>, but if the slice passes through the apex of the pyramid, that shape is a <em>triangle</em>.
(Image source: MathCaptain.com)
<u>Given</u>:
The point P' is the image of the point P under the translation
The coordinates of the point P are (6,0)
We need to determine the coordinates of the point P'
<u>Coordinates of the point P':</u>
The coordinates of the point P' can be determined by substituting the coordinates of the point P(6,0) in the translation.
Thus, substituting the coordinates, we have;
Simplifying the coordinates, we get;
Thus, the coordinates of the point P' is (0,-1)
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.