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Linear Algebra
Linear algebra is the detailed study of vector spaces. With applications in such disparate fields as sociology, economics, computer programming, chemistry, and physics, including its essential role in mathematically describing quantum mechanics and the theory of relativity, linear algebra has become one of the most essential mathematical disciplines for the modern world. Please direct all questions regarding matrices, determinants, eigenvalues, eigenvectors, and linear transformations into this category.
2,176 Questions
What is blank divided by blank which equals two divided by blank which equals 315?
One possible answer:
Blank 1 = 3150
Blank 2 = 10
Blank 3 = (2/315) = approx 0.006349
Wyy is a square is always symmetric?
Because a square has all equal sides. Thus by cutting in half, it will always be symmetric.
What is meant by space vector modulation?
Space-vector (pulse width) modulation technique is a PWM technique for three-phase voltage-source inverters.
Read the white paper I linked below, or the app note that I also linked below.
Interested in the real nitty gritty? Try the PhD Thesis that I linked below.
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
What is the slope of the line that passes through the points -8 -6 and 2 -3?
slope is y2-y1 / x2-x1
i.e. -3--6/2--8 = 3/10 i.e. 0.3
How do you graph this inequality m plus 2 6?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "less than", etc.
What is the y-intercept f 4y equals 4x-8?
First, you have to get y by itself by dividing each side by 4:
4y=4x-8
y=x-2
Then, the x-coordinate must equal zero if it is a y-intercept, so substitute 0 for x:
y=0-2
y=-2
The y-intercept would be (0, -2 )
How do you identify 2 solutions to a linear equation?
A linear equation is that of a straight line. Any one of the infinitely many points on the line will be solutions.
If the equation is in terms of the variables x and y, just pick any two values of x, solve for y and the results will be the coordinates of two solutions.
When a variable is by it self do you put a one next to it?
no. It is generally known that a single variable represents 1 of that variable.
A graphic solution is when you answer a question by graphing.
What is the unit rate of 120 miles in 2 hours?
1 mile per minute,
88 feet per second,
60 miles per hour.
How do you solve linear combination 5x equals 4y-30 and 2x plus 3y equals -12?
Here is one possible method of solving the system: 5x = 4y - 30
2x + 3y = -12
Rewrite to line up variables:
5x - 4y = -30
2x + 3y = -12
Multiply the top equation by 2 and the bottom equation by 5:
10x - 8y = -60
10x + 15y = -60
Subtract the two equations:
-23y = 0;
So y = 0; plug back into an original equation to find x:
2x + 3(0) = -12
2x = -12
x = -6The solution to the system is x = -6 and y = 0, or the point (-6,0).
How do you find the nth term of decreasing linear sequence?
The answer depends on what information you have.
If you know the first number, a, and the common difference d, (where d is negative), then the nth term is
a + (n - 1)*d : exactly the same as in an increasing linear sequence. The only difference is that d is negative instead of positive.
Why is slope so important in life?
Slope is important because it tells the steepness of a rollercoaster or can be used to figure out how high or tall something is!
How do you complete a table of values for y equals -2x?
Have certain numbers for x, substitute and then simplify.
Ex.
x
y= -2x
y
0
-2(0)= 0
0
1
-2(1)=-2
-2
2
-2(2)=-4
-4
3
-2(3)=-6
-6
Would radical 6 times 4 equal radical 24 or would it equal 4 radical 6?
Either answer is correct, depending on the parentheses that should have been specified.
sqrt(6*4) = sqrt(24)
sqrt(6)*4 = 4*sqrt(6)
When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
Why does the ratio of rise and run in a linear function always the same?
The ratio of rise and run in a linear function (which its graph is a nonvertical line) is called the slope of the line. We can calculate the slope of the line by using any two points on the line and always the ratio of changes on their y-coordinates and the changes on x-coordinates (rise and run) is constant (unchanged). The reason is that two points determine a line and its direction, so the line is fixed and extends without end in that direction. Any line intersects the x-axis only at one point (we call it the x-intercept point) by forming an angle α (the inclination angle), where 0˚ ≤ α < 180˚, that is measured from the positive x-axis to the line. There is a theorem that state that the slope of a nonvertical line is the tangent of its inclination: m = tan α if α ≠ 90˚ (if α = 90˚, then the line is vertical and has no slope).
