Let's consider an arbitrary 2x2 matrix as an example,
The columns of
are linearly independent if and only if the column vectors
are linearly independent.
This is the case if the only way we can make a linear combination of
reduce to the zero vector is to multiply the vectors by 0; that is,
only by letting
.
A more concrete example: suppose
Here,
and
. Notice that we can get the zero vector by taking
and
:
so the columns of
are not linearly independent, or linearly dependent.
First you can solve for b: Subtract a on both sides and get 2b=-a+10, then divide by 2 to get b by itself and get: b=-1/2a+5
Then you can plug in this equation for b in the other: This would give you: 2a+-1/2a+5=6. Then you can use that equation to solve for a and get: 1.5a+5=6, subtract 5, 1.5a=1, divide by 1.5, a=1/1.5
Then you can plug in the value of a to solve for b.
Answer:
Step-by-step explanation:
Probability (P) is calculated as
P = 
The first required outcome is a red sweet from a total of 3 + 5 = 8
P( red) = 
There are now 2 red left and a count of 7, since 1 has been eaten, thus
P( second red ) = 
P( red and red ) = × = 
=
If you factored this the outcome would be,
(q+3)(3p^2-4)
Answer: 
Step-by-step explanation:
Here, According to the question, The population of the world is 4 billion (approx).
Again According to the question, The world's population has grown at an average rate of 1.9 percent per year since 1945.
Therefore, after 1975 the growth rate will remains same.
Thus, the population of the world after t years,
(By the formula 
)
⇒
Where 1.019 is the growth rate and 4 billion is the initial population.
