Linear Algebra

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You mean this x2?

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There is no equation to solve!

actually MATRICES is the plural of matrix which means the array of numbers in groups and columns in a rectangular table...

and determinant is used to calculate the magnitude of a matrix....

Because to completely describe it you must know both how strong it is (magnitude) and in what direction it points.

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Absolute value looks like | x | and means that no matter what x is, the answer is positive. Unless it looks like this, -|x|, in which case it'll be negative. Also if you are talking about graphing it looks like a "V".

That will result in "replications" of the experiment.

because of d corrosion.....the constituent of the pulp(probably iron) reacts wid air to form iron oxide.....and the pulp turns black

In 1773, Joseph Louis Lagrange introduced the component form of both the dot and cross products in order to study the tetrahedron in three dimensions

No.

For example, the solution to

x ≤ 4

and

x ≥ 4

is x = 4.

It depends on what the dot product is meant to be equal to.

Placing a question mark at the end of a list of expressions or numbers does not make it a sensible question. Try to use a whole sentence to describe what it is that you want answered.

Eq 1: 3x + y = 10

Eq 2: 3x - 2y = -5

Subtract 1 from 2: -3y = -15

Divide by -3: y = 5

Substitute y = 5 in Eq 1: 3x + 5 = 10 so x = 5/3

Confirm in Eq 2: 3 x 5/3 - 10 = 15/3 - 10 = 5 - 10 = -5.

QED

Step 1: Draw two lines (axis), one across and one vertical.

Step 2: Pick a value of X (for example 1). Replace X with 1 and find the Y.

Step 3: Draw a point at the X,Y coordinated (X across and Y up).

Step 4: Repeat Steps 2 and 3.

Step 5: Draw a straight line through those points.

x + 2y = -5

2x + 3x = -9

5x = -9

x + 2y = -5

x = -2y - 5

5(-2y - 5) = -9

-10y - 25 = -9

-10y = 16

y = -5/8

x = -2y - 5

x = -2(-5/8) - 5

x = -5/4 - 5

x = -25/4

(-25/4, -5/8)

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".

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", "equals", "squared", "cubed" etc.

"Linear" equations are simply those where the highest power of any variable is 1 (one). There could be 2 variables in which case it is a straight line, or there might be three in which case it is a flat plane, or there might be a million in which case we don't know what it actually looks like.

Any system of linear equations can have the following number of solutions:

0 if the system is inconsistent (one of the equations degenerates to 0=1)

1 if the system is linearly independent

infinity if the system has free variables and is not inconsistent.

The history of modern linear algebra dates back to the early 1840's. In 1843, William Rowan Hamilton introduced quaternions, which describe mechanics in three-dimensional space. In 1844, Hermann Grassmann published his book Die lineale Ausdehnungslehre (see References). Arthur Cayley introduced matrices, one of the most fundamental linear algebraic ideas, in 1857. Despite these early developments, linear algebra has been developed primarily in the twentieth century.

We have three methods.

1) Cramer's rule method (Or) Determinant method

2) Rank method

3) Matrix Inversion method.

see the text book of 12th standard mathematics in tamilnadu text book corporation.

My own question: For just 2 unknowns, do any of the above include the "ordinary" way in which you multiply one or the equations through so one of the unknowns match in both lines, subtract, solve the now-single difference for its unknown then substitute back? Or do the above only apply if you're solving great banks of equations simultaneously.

It's the only method I know but I recall being taught how to stretch it to 3 unknowns, but it becomes rather long-winded.

I ask out of curiosity because I "learnt" matrices without understanding them and with only the haziest hint that they have any uses!

in mathematics the cross products are the binary operation on two vectors in a 3dimensional Euclidean space that results in another vector which is perpendicular to the containing the 2 inputs vector.