In linear algebra, the rank of a matrix
A
A is the dimension of the vector space generated (or spanned) by its columns.[1] This corresponds to the maximal number of linearly independent columns of
A
A. This, in turn, is identical to the dimension of the vector space spanned by its rows.[2] Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by
A
A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
The rank is commonly denoted by
rank
(
A
)
{\displaystyle \operatorname {rank} (A)} or
rk
(
A
)
{\displaystyle \operatorname {rk} (A)}; sometimes the parentheses are not written, as in
rank
A
{\displaystyle \operatorname {rank} A}.
First simplify 3x + 12 - 6x to -3x - 12
Next subtract 12 from both sides
Next subtract -9 - 12 and that would be -21
Next divide both sides by -3
Next lets simplify the fraction -21/-3 into 21/3 since those two negatives make a positive.
Lastly simplify the fraction 21/3 to get the answer.
Answer: x ≥ 7
Answer:
C
A
Step-by-step explanation:
the lines intersect at (2,1)
parallel = no solution
Answer:
Graph y = 2x
Step-by-step explanation:
First, let's get the equation into standard form. Distribute the 2 on the right.
Next, we want the variable "y" to be alone, so we at 4 to both sides.
That is our equation in standard y = mx + b form. "m" is our slope, while "b" is our y-intercept. Above , we don't have a value for b, therefore the line passes through the origin.
We do, however, have a slope, which can be thought of as 
or rise over run. To represent this, we can rewrite our slope as:
Meaning in each interval, the line goes up by 2 units, and moves forward by 1.
