Answer:
is linearly dependent set.
Step-by-step explanation:
Given: 
is a linearly dependent set in set of real numbers R
To show: the set is linearly dependent.
Solution:
If 
is a set of linearly dependent vectors then there exists atleast one 
such that 
Consider 
A linear transformation T: U→V satisfies the following properties:
1. 
2. 
Here, 
∈ U
As T is a linear transformation,
As is a linearly dependent set,
for some 
So, for some
Therefore, set is linearly dependent.
(a) Answer: One solution.
Explanation: two lines that have same slope with opposite sign will necessarily cross each other at a single point, as one is "pointing uphill" and the other "downhill."
(b) Answer: Infinitely many solutions.
Explanation:
2x + 3y = 5.5
4x + 6y = 11 | divide by 2
-->
2x + 3y = 5.5
2x + 3y = 5.5
--> equations are identical.
2x + 3y = 2x + 3y
so any (x,y) will satisfy this equation. This means infinitely many solutions.
(c) Answer: One solution
Explanation:
Continuing the two lines it becomes obvious they will cross at one point (the solution)
(d) Answer: No solution
Explanation: If the two lines are parallel, they will never cross (by definition of "parallel"). Therefore there will be no solution to the corresponding linear system.
Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function 
as compared to the graph of 
.
We can write our transformed function as:
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
,
,
Scaling of a function: 
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
The answer is 10
The equation would look like
5(4)-4(3)+2
And if you solve it, you’ll get 10 as your answer
Answer: 1050
Step-by-step explanation:
Number of combinations of selecting r things out of n = 
such that 
Given: A restaurant menu has 5 kinds of soups, 7kinds of main courses, 6 kinds of desserts, and 5 kinds of drinks.
If a customer randomly selects one item from each of these four categories, then by fundamental counting principle , the number of different outcomes are possible = 
hence, total number of outcomes = 1050
