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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
Yes it is. In fact, every singular operator (read singular matrix) has 0 as an eigenvalue (the converse is also true). To see this, just note that, by definition, for any singular operator A, there exists a nonzero vector x such that Ax = 0. Since 0 = 0x we have Ax = 0x, i.e. 0 is an eigenvalue of A.
Is 3x equals 8y a linear equation?
Yes, the equation 3x = 8y is a linear equation. A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power. In this case, both 3x and 8y fit this definition, making it a linear equation.
Oh, dude, you're hitting me with the tough math questions, huh? Well, technically, 1 half times 2 is just 1 because half of 2 is 1. But hey, who's really keeping track of fractions anyway, am I right? Math, like, totally not my strong suit, man.
How do you write Twelve Million Twelve thousand twelve?
Oh, dude, you write Twelve Million Twelve Thousand Twelve as 12,012,012. Easy peasy lemon squeezy. Like, just throw in some commas every three digits starting from the right, and you're good to go. Math and stuff, you know?
What is The product of 8 and 65?
The product of 8 and 65 is calculated by multiplying the two numbers together. In this case, 8 multiplied by 65 equals 520. Multiplication is a basic arithmetic operation that involves repeated addition of one number to itself a certain number of times, as specified by the other number.
What is the relationship between x and y in a non-linear graph?
I believe one of the relationships between x and y in a non-linear graph will be the slope of each point will be unproportional. Therefore, it will create a non-straight line (usually a curved line) on the graph. If it's a linear graph, the slope is proportional and the line will be straight. If anyone thinks this is not "straight to the point", please feel free to correct this.
{Added}. You are correct! The non-linear trace is curved. Linear means the trace is a straight line, produced when the y values are controlled by straightforwardly multiplying each x value by a constant which can be any number (except of course, 0).
A non-linear graph is one in which the y ordinates are controlled by x^N where N is not equal to 1, by a trigonometrical or logarithmic function of x; or in the particular case of the Hyperbola, the reciprocals of the x values.
What happens though in y = x^N when N does = 0? I'll leave it to you to spot the result - you don't need to calculate or plot it to realise the answer!
What is the standard form of negative square root of 5i?
The standard form of a complex number is a+bi.
So the standard form of the negative square root of 5i is 0-√(5i).
What is the number 9000000000000000000000000000 called?
The number 9000000000000000000000000000 is called nine octillion in the short scale naming system. In the long scale naming system, it is called nine quadrillion. The short scale system is commonly used in the United States and most English-speaking countries, while the long scale system is used in some European countries.
What do you call a four-sided polygon with four parallel sides the same length?
The four sides are NOT parallel.
If the fours sides were parallel , it would NOT be a polygon., but just four lines.
The opposite sides are parallel. Being the same length, it could be either a 'SQUARE' or a 'RHOMBUS'.
The difference being that the square has four right angles (90 degrees)-.
A Rhombus has the opposite angles the same, but not a 90 degrees.
What is the product of (3.7 104) and 2?
To find the product of (3.7 x 10^4) and 2, you first multiply the two numbers: 3.7 x 10^4 = 37,000. Then, you multiply this result by 2: 37,000 x 2 = 74,000. Therefore, the product of (3.7 x 10^4) and 2 is 74,000.
Which two upper case letters are formed with only two perpendicular line segments?
The letters T and L are formed as asked.
l and t from fiona1234
How do you write 0.356 in word?
To write 0.356 in words, you would say "zero point three five six." The number to the left of the decimal point is read as a whole number, followed by "point" for the decimal point, then each digit to the right of the decimal point is read individually.
What is word equation for 2HgO --- 2Hg O2?
Well, darling, the word equation for 2HgO turning into 2Hg and O2 is simply "mercury(II) oxide decomposes into mercury and oxygen." It's as straightforward as that, no need to complicate things. Just like a fine wine, chemistry is best enjoyed when kept simple and to the point.
Is y-2.5x a proportional relationship or no?
A proportional relationship exists when two variables are related by a constant ratio. In the expression y-2.5x, there is no constant multiplier connecting y and x, indicating a non-proportional relationship. If the relationship were proportional, the expression would be in the form y = kx, where k is a constant.
Oh, dude, 3x4t is just 12t. Like, you just multiply 3 and 4 to get 12, and then you tack on that "t" at the end because it's hanging out there, lonely and wanting to be part of the math party. So, yeah, 12t is the answer.
What is an example of linear multimedia?
An example of linear multimedia is a narrated slideshow presentation where the content progresses in a predefined sequence without user interaction. This type of multimedia typically follows a linear storyline or educational structure, guiding the viewer through a series of slides or frames in a specific order. Linear multimedia is commonly used in online courses, tutorials, and storytelling formats where a sequential flow of information is essential for understanding the content.
What are 3 consecutive even numbers that add to 6?
There are none.
1 + 2 + 3 = 6
However '1' & '3' are odd numbers.
Is there any direction associated with the dot product of two vectors?
No. The dot product is also called the scalar product and therein lies the clue.
What refers to the degree of slant or steepness?
The coefficient of the unknown variable in the equation.
I need at least 9 word problems for order of operations for my project and the equation and answer?
Well then, you'd better get to work ! That's a fascinating project, by the way.
How do you know if two matrices can actually be multiplied?
The number of columns in the first matrix must equal the number of rows in the second.
Who was the person responsible for the development of the Lamborghini?
Ferruccio Lamborghini, I think.
