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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
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What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
What is the coefficient in a linear equation called?
Due to some perversity in human nature, it is called a coefficient!
y = 1/3x+4/3
What are two ways to determine if an equation is linear?
All the variables that appear in it have the exponent 1.
If you plot the equation, it is a straight line.
What is the general form of linear equation in two variable?
ax + by + c = 0 where x and y are the variables, a, b and c are numerical constants.
Is the sum of the square of cross and dot products equal to the square of their product?
Your question makes no sense.... What you meant to say is:
Is the sum of the square of magnitude of the cross product and the square of dot product of two vectors equal to the product of the square of their magnitudes?
i.e:
|A x B|2 +(A .B)2 = |A|2|B|2
The answer is YES. It is called Lagrange's identity and is a special case of the Binet-Cauchy identity.
(Ax B) .(Cx D)+(A.D)(B.C)=(A.C)(B.D)
Where A= Cand B= D.
Linear
Is the pitch of a note a linear function of the length of the bar?
It's not clear what bar you're referring to. The "measure" in music is often colloquially
referred to as a "bar", but that clearly has nothing to do with the pitch of the notes
in it.
-- The only reasonable one I can think of is the bar of metal you tap with a hammer to
produce a tone. In that case, as long as the cross-section and the material composition
of the bar don't change, the pitch of the note you get out of it is inversely proportional to the length of the bar.
-- How about the bars on a xylophone, marimba, kalimba, vibraphone, etc. The above comments apply.
-- The pitch of the notes has no connection to the size of the drinking establishment in which
they are played or sung.
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The paper given by the attached link claims that a bar in a xylophone produces a collection of frequencies that are inversely proportional to the square of the length of the bar.
What is inverse of 2x2 matrix A can you find the inverse of any given matrix?
The inverse of a 2x2 matrix:
[a b]
[c d]
is given by
__1___[d -b]
ad - bc [-c a]
ad - bc is the determinant of the matrix; if this is 0 the matrix has no inverse.
The inverse of a 2x2 matrix is also a 2x2 matrix.
The browser used here is not really suitable to give details of the inverse of a general matrix.
Non-singular square matrices have inverses and they can always be found. Singular, or non-square matrices do not have a proper inverses but canonical inverses for these do exist.
Solution for the inequality x2 - 5x plus 6 0 is?
x2 - 5x + 6 = 0
(x - 2) (x - 3) = 0
x - 2 = 0 5 × 69 or x - 3 = 0
x = 2 or x = 3
Must solutions to systems of linear equalities satisfy both equalities?
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
What property of equality would be used to solve the equation -3x equals 252?
The multiplicative property of equality. Multiply each side by -1/3.
Can linear equations and linear inequality be solved the same way?
Basically.
If the inequality's sign is < or ≤, then you shade the part under the line.
If the inequality's sign is > or ≥, then you shade the part over the line.
What distinguishes a linear function from other functions?
A linear function is one in which the power of the function is only one. So, the graph of it would be a straight line. For example, x2 + x = y is not linear, because the highest power is 2. A main difference is, non linear functions have curves, where as a linear function is a straight line, with the exception of when the function has a power of 0, and it is technically a straight line.
What types of solutions can be found for linear equation?
A linear equation has a n infinite number of solutions. The coordinates of each point on the line is a solution.
The residual for a particular point in a regression is negative if the estimated or fitted value at that point is greater than the observed value.
relevant to a hypothesis, either
positively or negatively.
2.2 Hypotheses and Sub-hypotheses
Hypotheses are questions or conjectures of interest to an
observer. Hypotheses may involve alternative possible
explanations, possible answers, or alternative estimates.
Hypotheses may have substructure. It is sometimes possible to
partition a high-level hypothesis into a set of sub-hypotheses. The
substructure decomposition is always a hierarchical tree. The
hierarchy may be several levels deep before bottoming out in
questions that can be directly assessed and answered by evidence.
What does y-x-2 look like on a graph?
You could not graph (y-x-2) because it has no equal sign in it. In order to graph an equation, there must be a value that the numbers and variables are equal to. (e.g. y=2x+3)
How many solutions does a nonlinear system of equations?
None, one or many - including infinitely many.
Does a graph of a system of equations intersect more than 1 point?
In some special cases lines can end up intersecting each other at every point, which means the two seperate lines are on top of each other, where you end up having infinite solutions
