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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
How do you solve 2x-3y5 and -6x 9y12 using the linear sombination method?
This system is inconsistent. There is no solution.
2x - 3y = 5
-6x + 9y = 12
Multiply the top equation by 3:
6x - 9y = 15
add the two equations together:
6x - 6x - 9y + 9y = 5 + 12
0 = 17
Which is a contradiction. Therefore the lines never intersect, and the solution is the empty set.
How do you write 0.955 as a percentage?
0.955 written as a percentage is 95.5%. Whenever you turn a decimal into a percentage, move the decimal over two times to the right.
How do you find a general statement for Lacsap's Fractions?
if you want a detailed answer... you must pay, you can contact me if you are in the philippines. i know the answer.
How are linear inequalities and linear equations the same?
They are not. An inequality cannot, by definition, be the same as an equation.
What is the answer of the linear combinations of 5x 9y6 45 and 2x-7y5?
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".
How much is 2 to the power -2?
2 to the power of -2 is equal to 1/4.
x to the power of -y is equal to 1/xy.
What are the elementry matrices?
An elementary matrix is a matrix obtained from the identity matrix following one of the following row operations:
- Swap 2 rows;
- Multiply any row by a non-zero constant;
- Replace a row by the sum of itself and a non-zero multiple of another row.
How do you do the equation 4dividedby3 pi radius cubed Example please?
It's used in finding the volume of a sphere which is: Volume = 4/3*pi*radius3
What are the effects of co relation on linear transformation?
Correlation has no effect on linear transformations.
How solve systems of equations?
The answer will depend on the nature of the equations and the level of your knowledge.
Probably the simplest way to deal with a general problem is to do it graphically. As long as you can calculate the values of the equations, you can plot them and the solutions are a subset of the points of intersection.
If the equations are all linear and do have a solution then inverting the matrix of coefficients is probably simplest way. In some respects this is like
- selecting one equation,
- using it to express on variable in terms of the others,
- substituting the expression for that variable in all the other equations.
That reduces the number of equations and variables by one. Continue until you have just one variable whose value you can determine. Substitute this value in one of the last two equations and you will then have two known variables. Go back up the line until you have them all.
What is the rule for the sequence 3.7 3.2 2.7 2.2?
The difference between successive terms is 0.5.
You could write this as tn+1 = tn - 0.5 and t0 = 3.7
or tn = 3.7 - n/0.5, for n = 0, 1, 2, ...
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How do you solve the problem -2y 5y10?
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".
How far back will a 12 lb ball be while being dragged from a boat going 3 miles per hour 40 ft down?
The difficulty with your question is that it does not clearly define the problem. For example, a 12 pound ball made of lead will weigh the same as a 12 pound ball made of balsa wood, but the balsa wood ball (measuring several feet across) will float where the 12 pound ball made of lead will measure just a couple inches across and sink readily. To further complicate things, the line (rope or chain) you use to drag the ball also creates drag just as the ball would do. The size of the line and what it is made of is important, too, because the line will hang in what is called a catenary, a kind of sag in the line. There is a formula for the catenary, a formula for the drag on the ball, and a formula for the drag on the line, itself.
The final consideration is the consistency of the sea bottom. Dragging a ball through kelp will be different than dragging a ball across packed mud or loose gravel.
There are many things to consider besides speed, depth, and weight of a ball. Put all that together and then you mightget a close answer to what you seek.
To give you an idea that will get you in the ball park, so to speak, assume that the line drags out to an exact triangle. There are three sides to the triangle: a, b, and the hypotenuse (c). Assuming the drag will cause a 45 degree angle, then the depth down (a) will be the same as how "far back" the ball is (b) and the hypotenuse (how long the line is) will be the square root of the sums of the squares of the two sides (c). That is, as the Scarecrow quoted Pythagoras in the Wizard of Oz, "The square of the hypotenuse is equal to the sums of the squares of the other two sides!" In this case, two times forty squared is 3200 and the square root of that is just over 56 1/2 feet. But, remember: this won't be anywhere near where a real ball and line will be. The problem is more complex than a lesson from the Scarecrow.
~Let us not forget to include the salinity of the waters involved, which would affect the bouyancy of any items in it. Plus, whether or not this alleged ball is actually round, or somehow oval in shape. Plus; 40 feet down and how far outwill make yet another difference to your recalculations.
