Completely factored form of xy^3 – x^3y?
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
By drawing the point (-3,-1) in the coordinate plane we find the graph shown below. Since there are 10 points between points A and B, we need to start at point A and then we have to move 11 units either to the right, to the left, up, or down .
1. MOVING TO THE RIGHT:
From point A, move 11 units horizontally to the right to come to point B:
(-3+11, -1) = (8, -1)
2. MOVING TO THE LEFT:
From point A, move 11 units horizontally to the left to come to point B:
(-3-11, -1) = (-14, -1)
3. MOVING UPWARD:
From point A, move 11 units vertically upward to come to point B:
(-3, -1+11) = (-3, 10)
4. MOVING DOWNWARD:
From point A, move 11 units vertically downward to come to point B:
(-3, -1-11) = (-3, -12)
So this are the basic movements you can get to find point B. You also can move diagonally upwards or downwards in whose case you would find other four points. The graph below shows a red point which is A, and the other points are in black color and represent B.
A. False. Consider the identity matrix, which is diagonalizable (it's already diagonal) but all its eigenvalues are the same (1).
b. True. Suppose
is the matrix of the eigenvectors of 
, and 
is the diagonal matrix of the eigenvalues of :
Then
In other words, the columns of
are 
, which are identically 
, and these are the columns of 
.
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue
and eigenvector 
, where 
. But the matrix can't be diagonalized.
b. True. Suppose
Then
In other words, the columns of
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue