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.
Answer:
x = 14.7
Step-by-step explanation:
Use Law of Sines.
7/sin20=x/sin46
cross multiply
7sin46=xsin20
divide both sides by sin20 to isolate x
x = 7sin46/sin20
x = 14.72
Answer:
88 adult tickets were sold
Step-by-step explanation:
3s + 7a = 1102
(s + a = 250)-3
3s + 7a = 1102
+ -3s - 3a = -750 Add these equations together
4a = 352 Divide both sides by 4
a = 88
Now plug this into the second equation
s + a = 250
s + 88 = 250
- 88 - 88 Subtract 88 from both sides
s = 162
If this answer is correct, please make me Brainliest!
Notation. x y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means x is greater than y. The last two inequalities are called strict inequalities. Our focus will be on the nonstrict inequalities. Algebra of Inequalities Suppose x + 3 < 8. Addition works like for equations: x + 6 < 11 (added 3 to each side). Subtraction works like for equations: x + 2 < 7 (subtracted 4 from each side). Multiplication and division by positive numbers work like for equations: 2x + 12 < 22 =) x + 6 < 11 (each side is divided by 2 or multiplied by 1 2 ). 59 60 4. LINEAR PROGRAMMING Multiplication and division by negative numbers changes the direction of the inequality sign: 2x + 12 < 22 =) x 6 > 11 (each side is divided by -2 or multiplied by 1 2 ). Example. For 3x 4y and 24 there are 3 possibilities: 3x 4y = 24 3x 4y < 24 3x 4y > 24 4y = 3x + 24 4y < 3x + 24 4y > 3x + 24 y = 3 4x 6 y > 3 4x 6 y < 3 4x 6 The three solution sets above are disjoint (do not intersect or overlap), and their graphs fill up the plane. We are familiar with the graph of the linear equation. The graph of one inequality is all the points on one side of the line, the graph of the other all the points on the other side of the line. To determine which side for an inequality, choose a test point not on the line (such as (0, 0) if the line does not pass through the origin). Substitute this point into the linear inequality. For a true statement, the solution region is the side of the line that the test point is on; for a false statement, it is the other side.
Answer:
<h2>a) |-13 - (-4)|</h2>
Step-by-step explanation:
The formula of a distance between two points (numbers) A and B on the number line:
d = |B - A| = |A - B|
We have A = -13 and B = -4. Substitute:
d = |-13 - (-4)|
