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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 the purpose of locating the circumcenter?
It identifies the point which is equidistant from the three vertices of the triangle. If, for example, you wanted to locate a phone mast to supply three remote locations, a good starting point would be to find somewhere which is at or very close to the circumcentre. Of course, local geography (hills, for example) would have to be taken into account.
How do you find inverse of the matrix using augmented matrix?
your first step is to augment(connect with the bar in between) the identity matrix onto the right side of the original matrix
then your main objective is to turn your original matrix into the identity matrix while only using elementary row operations
elementary row operation rules:
- row swap- you can swap any row with another row. meaning the entire first row can be swapped with the second, or third row but only entire rows may be swapped
- row multiplication- you can multiply or divide entire rows by a constant ex: if row1=3t-5s then row1 x 2=6t-10s (note you must multiply every term in the variable)
- row addition- any row can be added or subtracted onto another row to change that row. note if you were to add row1 to row2 for example change would only be done to row2 not row1. (very important)- be careful when adding rows remember that when rows are being added/subtracted, they subtract according to how columns within rows align with. this is where the most mistakes happen.
- (most important)- what ever action you perform on a row you do it to the entire row. you must treat both sides of the line as ONE UNIT(thasshow i remembered). when you perform an operation on the original matrix, you cannot forget to do the same to the augmented peice
if the original matrix is sucessfully changed into the identity matrix using these rules, then you should end up with the identity matrix on the original side and theinverse matrix on the augmented side
examples of this method can be found by looking up linear algebra on khanacadamy.org
What number goes into 26 and 18?
The only common factors I can see are 1 and 2. 18 is divisible by 1,2,3,6, and 9, and 26 is divisible by 1,2,13,and 26.
How do you use logarithm tables for division?
Suppose you want to divide x by y
Find log(x) and log(y) to any base b (usually 10 or e)
Calculate z = log(x) - log(y)
Look up the antilog of z (or find the number whose log is z).
x/y = antilog(z)
What quadrant do points lie if their abscissa is positive and ordinate is negative?
The fourth quadrant
Why is it important the linear equations and inequalities?
There are many simple questions in everyday life that can be modelled by linear equations and solved using linear programming.
If it has infinite number of solutions that means that any ordered pair put into the system will make it true. I believe the relationship of the graphs question your asking is that tooth equations will probably be the same line
Can you find the equation of a line containing the given pair of points 3 2 and 9 3?
Assuming it's a straight line (y=mx+b or Ax+By+C=0) then we will:
1. Find the slope of the line using the slope formula.
y2-y1/x2-x1=m (keep in mind that the bigger value does not necessarily have to be y2 or x2, you will end up with the same "m" value regardless)
2-3/3-9=m
-1/-6=m
1/6=m
2. Calculate vertical shift (b value).
Sub a point into the equation y=(1/6)x+b (It does not matter which point you use, again, either one will work)
2=(1/6)(3)+b (I used the point (3,2) in this instance)
2=(3/6)+b
2=(1/3)+b
2(3)=b
b=6
3. Write the equation.
y=(1/6)x+6
How long is the diagonal of a 12ft-by16-ft rectangular garden?
this is the pythagorean theorem: x^2 + y^2 = c^2.
1) 12^2 + 16^ = c^2
2) 144 + 256 = c^2
3) 400 = c^2
4) Take the sq. root of both sides.
5) 20 = c
Can the solution of a system of linear inequalities be the point of a line explain?
It's pretty much always the point of a line because the soulution of the system is always an ordered pair where the two or more lines intersect
What inequality means no less than?
The > symbol represents less than. For example, x>y represents x is greater than y.
It is the input value to the function called "f(x)"
If f(x)= x + 1, an input value of 2 ( x equals 2) would give us 2 + 1, or 3.
What methods can be used to solve a system of equations?
The answer depends on the nature of the equations. For a system of linear equations, the [generalised] inverse matrix is probably simplest.
For a mix of linear and non-linear equations the options include substitution, graphic methods, iteration and numerical approximations. The latter includes trail and improvement.
Then there are multi-dimensional versions of "steepest descent".
Are calculus and linear algebra courses hard for an individual who got an a plus in algebra?
you don't go from algebra to calculus and linear algebra. you go from algebra to geometry to advanced algebra with trig to pre calculus to calculus 1 to calculus 2 to calculus 3 to linear algebra. so since you got an A+ in algebra, I think you are good.
Is 24x 3 -5x the same as 3x 3?
- No they are not the same.
- For example, for x =1: 24x3 -5x = 72-5 = 67 while 3x3 = 27
15 quarters, 3 dimes
What is the difination of linear function?
A linear function is any function that graphs to a straight line. What this means mathematically is that the function has either one or two variables with no exponents or powers. If the function has more variables, the variables must be constants or known variables for the function to remain a linear function.
What are advantages of solving equations without calculators?
Calculators won't read variables, so you have to put in the number it is equal to yourself.
What is the first step in solving the following system of equations by substitution?
The first step is to show the equations which have not been shown.
How do you find for the zero of a linear function?
If it is a linear function, it is quite easy to solve the equation explicitly, using standard methods of equation-solving. For example, if you have "y" as a function of "x", you would have to solve the variable for "x".
How are linear equations and linear inequalities similar?
A linear equation corresponds to a line, and a linear inequality corresponds to a region bounded by a line.
Consider the equation y = x-5.
This could be graphed as a line going through (0,-5), (1,-4), (2,-3), and so on. The inequality y > x-5 would be the region above that line.
