5. Which unit is used to measure volume? Hours Feet Gallons Tons
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:
Given:
To solve for y, let us first isolate y on one side of the equation. We can do this by subtracting from the left and move it to the right. We then get:
Now, we have y isolated. We now have to remove the 4 from the y. The only way to do this is divide both sides by 4. We then get our final answer:
We can clean this up by putting it in a common form, slope-intercept form: