0
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
When graphing a linear inequality the first step is to replace the inequality symbol with what sign?
With the equal sign (=).
If you mean: 3x-4y = 19 and 3x-6y = 15
Then: x = 9 and y = 2
What is the best estimate of 512 25?
The best estimate is the true value.512 = 2^9 = 2^7*2^2 = 128*4
Then 512*25 = (128*4)*25 = 128*(4*25) = 128*100 = 12800.
When should you use a multiplication to solve a system of linear equestions by elimination?
When the coefficients of the variables in the linear equations are different.
If
eqn(A): ax + by+ cz + ... = m, and
eqn(B): px + qy + rz + ... = n
where x, y z are variables and the rest are constants, then
p*eqn(A) = pax + pby+ pcz + ... = pm and
a*eqn(B) = apx + aqy + arz + ... = an
The coefficients of x, pa and ap, are equal and so subtracting one equation from the other will eliminate x.
The quotient works out as: x^2+2x+4 and there is a remainder of -3
List three methods used to solve systems of equations?
1. Solve one equation for one of the variable. Replace the variable for the equivalent expression, in the remaining equations.2. Add one equation (possibly multiplied by some factor) to another equation, in such a way that one of the variables get eliminated.
For the specific case of linear equations, there are several additional methods, for example using determinants, or matrices.
What is the classification of a system of equations?
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
How do you know that a table value is a linear function?
There are several ways to do that. For example, you can actually graph the function. Or, you can check the ratio of the differences between the points. If this ratio (change in y, divided by change in x) is constant, the function is linear.
What is the slope for y equals negative two over three x plus two?
If: y = -2/3x+2 then the slope is -2/3 and the y intercept is 2
How do tables show the solution to a system of equations?
Any answers that are the same in the both tables are answers that for both equations. y=x is (1,1), 2,2), (3,3) ... y=x^2 is (1,1),(4,2)... (1,1) is in both lists.
How do you move a squared variable that is the denominator to the other side of the equation?
It's the same as if you have anything else in the denominator. You can multiply both sides by the squared variable. Example (using "^" for "power"):
a = 1 / b^2
Multiply both sides by b^2:
Step 1: a b^2 = b^2 / b^2
Step 2: a b^2 = 1
How do you graph using the rate of change and initial value?
Normally on the Cartesian plane using as for example the straight line equation y = mx+c whereas m is the gradient or slope and c is the y intercept.
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
If f of x equals 3x - 10 then what is f of 2a?
if f(x) = 3x - 10, then whatever is put (substituted) for x in the "f(x)" bit is substituted for x in the "3x - 10" bit.
Thus f(2a) = 3(2a) - 10 = 6a - 10.
How do you solve x squared -4x equals 41?
x² - 4x = 41 → x² -4x - 41 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac))/(2a)
→ x = (4 ± √(4² - 4×1×-41)/(2×1)
→ x = (4 ± √(4(4+41)))/2
→ x = (4 ± 2√45)/2
→ x = 2 ± √45
→ x = 2 + √45 (≈ 8.708) or x = 2 - √45 (≈ -4.708)
Equations have solutions. I'll assume that's x^2 - 4x + 41 = 0 since this website can't reproduce plus or equals signs in questions. That doesn't factor neatly. Using the quadratic formula, we find two imaginary solutions: 2 plus or minus i times the square root of 37
x = 8.082762530298219i
x = -4.082762530298219i
where i is the imaginary square root of -1
no its is x^2-4x=41
Is it possible to have a system of linear inequalities where solution is every point in the entire?
Yes, you can say something like y < infinity and y > -infinity .
What equation is equivalent to 3x-4y equals 8?
3x - 4y = 8
Solve for x:
3x = 4y + 8
x = 4/3y + 8/3
Solve for y:
-4y = -3x + 8
y = 3/4x - 2
How would you factor 24x3 plus 72x2 plus 30x?
24x^3 + 72x2 + 30x = 6x*(4x^2 + 12x + 5)=6x*(2x + 1)*(2x + 5)
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
It is the input value to the function called "f(x)"
If f(x)= x + 1, an input value of 2 ( x equals 2) would give us 2 + 1, or 3.
