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.
CD, CE, HG, GF, AL, LB, AB, HF, DE. A line segment is comprised of any two points. The ones I listed are the ones specifically named in the picture.
Answer:
2,200 students
Step-by-step explanation:
To find the number of students, create a proportion which is two equal ratios. Since the middle school and the high school are proportional then they have equal ratios.
Solve for x by cross multiplying by multiplying the numerator and denominator of each fraction.
900(110) = 45(x)
99,000=45x
2,200 = x
As given Zahra has paper rectangles of different sizes.
Also, Every rectangle is 5 cm is longer than it's breadth.
So, if Length=L, then Breadth= L- 5
Or , if Breadth= B, then Length= B+5
or, if length is x and breadth is y ,then writing in terms of equation
→x=y+5
As you can see,there is not any proportional relationship between length and widths of these rectangles.
I take it you meant θ angle, anyway.
we know the tan(θ) = -4/7... alrite, we also know that 270° < θ < 360°, which is another to say that θ is in the IV quadrant, where the adjacent side or "x" value is positive whilst the opposite side or "y" value is negative.
