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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 64xsquared - 49 in factored form?
There is a formula for the "difference of squares." In this case, the answer is
(8x + 7)(8x - 7)
The equation of a parallel line is of the form 2x - y = c for some c.
(-3, -11) is on this lime so
2*(-3) - (-11) = c
-6 + 11 = c so that c = 5
and therefore, the equation is 2x - y = 5
What are the advantages of Identity matrix?
If the product of two matrices is an identity matrix then, one matrix is inverse of the other. i.e. AB = I then, A = B-1 and B = A-1
Inverse of matrix can be found by using these two results:
A = AI and A = IA.
By using these results inverse of a matrix can be found by applying same elementary row or column operation on both sides. A on R.H.S. remains as it is.
What is Linear and Non-Linear Relationships?
A linear relationship means that the slope of the line is proportional, which means that the line is straight. In contrast to the linear realtionship, the non-linear relationship's slope is not proportional and the line will curved and not straight. Formula of calculating the slope is the difference of y divided by the difference of x.
How do you solve -15X equals -5 times 3X plus 2?
-15x=-5*3x+2
-15x=-15x+2
+15x +15x
-----------------
0=2
How do you find where two lines meet on a graph by solving an equation?
You can't find this out by solving an equation, but you can by solving a system of two linear equations. Basically, you would need to know the equations for both of the lines before you began. Then, you would solve one of those linear equations for one of the variables in terms of the other, like y in terms of x. Then, you'd plug that value of y, in our case, into the other equation and solve for x. Then you'd plug that value of x, which is now a number, back into the original equation to get a numerical value for y. Your intersection point would then be the ordered pair (x,y). Here's an example:
2x + 14y = 8,
-6x + 10y = 4.
Solve the first equation for y:
y = (4/7) - (1/7)x.
Plug that value for y into the second equation:
-6x + (40/7) - (10/7)x = 4.
Solve for x:
(10/7)x + (42/7)x = (40/7) - (28/7),
(52/7)x = (12/7),
x = (12/52) = (6/26) = (3/13).
Plug that value of x into the first equation:
(6/13) + 14y = 8,
14y = (98/13),
y = (98/182) = (49/91) = (7/13).
So the point at which those two lines intersect would be the ordered pair (3/13,7/13).
Finally, it's usually worth while to verify your answer by plugging these values into the original equations.
2(3/13) + 14(7/13) = (6/13) + (98/13) = (104/13) = 8, so the first one's right.
-6(3/13) + 10(7/13) = -(18/13) + (70/13) = (52/13) = 4, so that one's right too.
What is the perpendicular line to y equals -6x plus 3?
y = -6x + 3
Multiply the slope by the negative reciprocal
y = 1/6x + 3
What number can go into 13 what number can go into 13 what number can go into 13?
Nothing goes into 13 evenly other than 1 and 13, so that means it is a prime number.
How do you get a slope and a linear function?
plotting a slope means plotting a graph of y against x.to get the linear function ,the only thing to do is to know whether the value of y and the equivalent value of x at the point if its a well plotted slope normally any choosen point will be the same .assuming it is not a curve.if not replot.
How do you calculate 1.04 to the 205 power?
Multiply 1.04 by itself (1.04) 205 times.
The answer is about 3,103.37714
Matrices are generally used to solve simultaneous equations. You use the co-efficient of the variables and arrange them in a matrix to solve them. To do so requires at least as many equation as there are variables. Other uses include vector calculations.
How do you graph y equals 4x plus 5?
You start at (0,0) on the graph. Go up vertically 5 and place a dot on (0,5). Then you go up 4 and to the right 1 and put a dot on (1,9). Then go up another 4 and to the right once more and put a dot on (2,13). Then using a ruler or straightedge, draw a line through all 3 dots.
Now to show you why!!
You always start at (0,0) on the graph. Then I went up five because it was plus 5, This just tells you where on the y axis to put your first dot!! Up 5 because it was y=4x+5. Then it gets a little tricky!! Lets for a second imagine the it was 4/1x. The number on top (4) is the rise or how many times you go up vertically! Then the number on the bottom (1) is how many times you go over to the right!! I don't know how to better explain thing without a showing a picture or drawing it!! Hope this helps!!
I bet it can be done, but I'll be darned if I can!
Which you don't want. You want the least common denominator, which is 360.
What is the variable number for 0.6 equals 3t?
We're not at all sure what you mean by "variable number".
If 0.6 = 3t, then t = 0.2 .
What is the difference between a 'dot product' and a 'cross product'?
Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.
a ● b = ║a║║b║cos(θ)
Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.
a X b= ║a║║b║sin(θ)n
