In the following exercises, plot each point in a rectangular coordinate system.
6.
(a)
(
0
,
1
)
(b)
(
0
,
−
4
)
(c)
(
−
1
,
0
)
(d)
(
0
,
0
)
(e)
(
5
,
0
)
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
The 2x2 linear system of equations -2x+4y = 8 and 4x-3y = 9 was put into the following
-2 4
8
augmented matrix:
4
-3
9
This augmented matrix is then converted to row echelon form. Which of the following matrices is the
appropriate row echelon form for the given augmented matrix?
0
Option 1:
1
11
-2
Option 2:
4
-3 9
Option 3:
10
܂
-2
-4
5
25
1
-2
-4
Option 4:
0 1
5
1 -2
Option 5:
0
0
20
-4
5
○ Option 1 is the appropriate row echelon form.
○ Option 2 is the appropriate row echelon form.
○ Option 3 is the appropriate row echelon form.
○ Option 4 is the appropriate row echelon form.
○ Option 5 is the appropriate row echelon form.
Let matrix A have order (dimension) 2x4 and let matrix B have order (dimension) 4x4.
What results when you compute A+B?
The resulting matrix will have dimensions of 2x4.
○ The resulting matrix will be a single number (scalar).
The resulting matrix will have dimensions of 4x4.
A+B is undefined since matrix A and B do not have the same dimensions.
If
-1
"[a446]-[254]
4b
=
-1
, find the values of a and b.
○ There is no solution for a and b.
○ There are infinite solutions for a and b.
O a=3, b=3
O a=1, b=2
O a=2, b=1
O a=2, b=2
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.