Answer:
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
Step-by-step explanation:
Just to add a bit more information, "Elimination" Can have a variety of other interpretations. Elimination techniques typically refer to 'row reduction' to achieve 'row echelon form.' Do not worry if you have not heard of these terms. They are used in Linear Algebra when referring to "Elimination techniques"
Gaussian Elimination
Gauss-Jordan Elimination
LU-Decomposition
QR-Decomposition
These techniques for elimination are preferred for 3rd order systems and higher. They use "Row-Reduction" techniques/pivoting and many subtle math tricks to reduce a matrix to either a solvable form or perhaps provide an inverse of a matrix (A-1)of linear equation AX=b. Solving systems of linear equations (n>2) by elimination is a topic unto itself and is the preferred method. As the system of equations increases, the "condition" of a matrix becomes extremely important. Some of this may sound completely alien to you. Don't worry about these topics until Linear Algebra when systems of linear equations (Rank 'n') become larger than 2.
Substitution is the preferred method for 2 equations in 2 unknowns. The constants are unimportant other than having a non-zero determinant. It is always easy to find multiplicative factors using LCMs of one variable or the other to allow substitution into the other equation:
Example:
4X + 5Y = 9
5X - 4Y = 1
Notice that 20 is a LCM of either the X or Y variable. So multiply the first by 4 and the second by 5 and then adding the two (Y's will drop out allowing for substitution)
4(4X + 5Y = 9)
5(5X - 4Y = 1)
Multiplying to produce the LCM factors:
16X + 20Y = 36
25X - 20Y = 5
Adding the equations
41X = 41
X = 1
Substitution into either equation yields
Y = 1
Elimination techniques are preferred for Rank-n>3
(0,0) and (1,0) are the x-intercepts.
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Based on the situation above the inequality will he use to contradict the assumption is <span>
4:10 ≠ 6:14</span>
if DE is parallel to BC
then
4: (4+5) = 6 : (6 + 8)
Answer:
Therefore,
The value of x is 5.97 cm.
Step-by-step explanation:
Given:
Let the length of side of Square be "x" cm'.
Radius of Circle be "r"
Area of Circle = 56 cm squared
pi = 3.14
To Find:
x = ?
Solution:
We know Area of Circle is given by,
Substituting the values we get
We have, a square fits exactly inside a circle with each vertices being on the circumference of the circle,
Vertex Angle of a Square is 90°.
In a Circle Diameter Subtends a Right angle,
So it's Diagonal will be the Diameter,
Substituting the values we get
Therefore,
Also we know that,
Length of Diagonal of a Square for side "x" is given by,
Substituting the values we get
Therefore,
The value of x is 5.97 cm.
The average rate of change is (total change in f(x))/(total change in x) so
r=(f(6)-f(2))/(6-2)
r=(36-6-4-4+2+4)/4
r=7
