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Algebra
Algebra I
Systems of equations

Recent questions in Systems of equations

Alfredeim 2022-09-15

Given the parameters $p_{1}, p_{2}, p_{3}$ does the following system can be solved:
This system actually discribes a Rotation Matrix
$p_{1} a b c p_{2} d e f p_{3}$
where only $p_{1}$ , $p_{2}$ and $p_{3}$ are know. For example $p_{1} = p_{2} = p_{3} = 1$ would result in $a = b = c = d = e = f = 0$ .
Why is this system (unabigiously) solvable / not solvable?
If it is solvable, what is the solution?

tamolam8 2022-09-12

Solve the system of equations in response write down the sum of the solutions of the system {4x-2y=2 and below 2x+y=5

manudyent7 2022-09-12

Suppose we are given the system of equations
$α_{1} A + β_{1} B + γ_{1} C = x$
$α_{2} A + β_{2} B + γ_{2} C + θ_{2} D = y$
$α_{3} A + β_{3} B + γ_{3} C + θ_{3} D = z$
where $α_{i}, β_{i}, γ_{i}, θ_{i}$ are chosen from finite field $F_{q}$ where $q$ is prime. Note that the variables here are $A, B, C, D$ .
Is it possible to use the equations above to have a unique solution for $A, B, C$ ?

mksfmasterio 2022-09-12

How to the fixed points of the following recurrence?
$X_{n} = 2 X_{n - 1} (2 - 3 X_{n - 1}) + X_{n - 1}$
And therein, determining their stability analytically?

Pavukol 2022-09-11

Transformation of inverse to a system of linear equations. Need to solve $X = (U^{'} W U)^{- 1} U^{'}$ . $U^{'}$ is $U^{'}$ is $7 \times 7$ positive definite matrix, $U^{'}$ is of rank $3$ .
Transformed $(U^{'} W U)^{- 1} U^{'}$ as
$(U^{'} W U)^{- 1} U^{'} W U = I X W U = I U^{'} W X^{'} = I (I \otimes U^{'} W) v e c (X^{'}) = v e c (I) .$
When I solved $X = (U^{'} W U)^{- 1} U^{'}$ and as the above linear system using $R$ , the answers are slightly different. Does something wrong with the above logic?

engausidarb 2022-09-11

Find (in case there is any) which complex vector $n$ of 2 dimensions, multiplied by its conjugate transpose, returns a diagonal matrix.
$n = [a, b]^{T} = [a_{1} + j a_{2}, b_{1} + j b_{2}]^{T}$
$n n^{†} = I$
Obtain the following set of 4 equations:
$a_{1}^{2} + a_{2}^{2} = 1$
$b_{1}^{2} + b_{2}^{2} = 1$
$a_{1} b_{2} + a_{2} b_{1} = 0$

Marley Blanchard 2022-09-11

Is there any simple analytic method for solving $\sqrt{x} + y = 7$ and $x + \sqrt{y} = 11$ simultaneously.

Andreasihf 2022-09-10

How to solve the system of equations $y = 5 x^{2} - 2 x$ and $y = 10 x + 9$ ?

tashiiexb0o5c 2022-09-10

Solve
[{2 + 2 ad + 2 ae == 0, 1 - 2 b + 2 db + 2 eb == 0, 1 + 2 dc + 2 ec == 0, -2 + a^2 - 2 b + b^2 + c^2 == 0, -2 + a^2 + b^2 + c^2 == 0}, {a, b, c, d, e}]
My rty:
$2 + 2 λ_{1} x_{1} + 2 λ_{2} x_{1} = 0$
$1 + 2 λ_{1} x_{2} + 2 λ_{2} x_{2} - 2 λ_{2} = 0$
$1 + 2 λ_{1} x_{3} + 2 λ_{2} x_{3} = 0$
$x_{1}^{2} + x_{2}^{2} - 2 x_{2} + x_{3}^{2} - 2 = 0$
$x_{1}^{2} + x_{2}^{2} + x_{3}^{2} - 2 = 0$

tamola7f 2022-09-10

Method to solve the following system of nonlinear equations?
$141, 3829 = A + \frac{B}{323} + 5, 78 C + F 323^{E} 69, 07645 = A + \frac{B}{333} + 5, 81 C + F 333^{E} 40, 55085 = A + \frac{B}{343} + 5, 84 C + F 343^{E} 27, 92544 = A + \frac{B}{353} + 5, 87 C + F 353^{E} 19, 7697 = A + \frac{B}{363} + 5, 89 C + F 363^{E}$
where $A, B, C, E, F$ are needs to be determined

souta5 2022-09-10

Provide non-trivial solution of the following:
$\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b}$
$a = ?, b = ?, c = ?$

jhenezhubby01ff 2022-09-09

If the subspace is described as the range of a matrix: $S = {A x : x \in R^{n}}$ , then the orthogonal complement is the set of vectors orthogonal to the rows of $A$ , which is the nullspace of $A^{T}$ . How to make the above claim from the definition of orthogonal complement as the set of vectors that are orthogonal to all $A x$ .

Spactapsula2l 2022-09-09

Let $a > b > c > 1$ . How to find solutions in positive numbers of the following system?
${\begin{cases} a x > y + z \\ b y > x + z \\ c z > x + y \end{cases}$

Deacon House 2022-09-09

Algebraic process to find numbers so that $x y = 45$ and $x + y = 18$
The sum of two numbers is 18 and their product is 45. Find the numbers.

Milton Anderson 2022-09-09

Solving a system of three equations: $d = s \cdot 3, c = s \cdot 1.5, c = 2 \cdot d$ .

peckishnz 2022-09-08

Given the system
$x^{'} = x e^{y - 3}$
$y^{'} = 2 \sin (x) + 3 - y$
Find the equilibrium points and decide if they are stable.
The equilibrium points of the system are the solutions $X$ such that $X^{'} = 0$ , which means $x^{'} = 0 = y^{'}$ ′. By this condition, I get the points $X = (x, y) \in {{(0, 3), (k π, 3)}, k \in Z}$ .

moidu13x8 2022-09-07

Equations:
${\begin{cases} K = \frac{B - 3}{20} \\ K = (20 S + 3) R + S \\ K = 20 S^{2} + (20 N + 7) S + N \\ N = R - S \end{cases}$
$B$ values, e.g: $834343, 3253538, 10^{87653}$
How to find the $R$ values?

drobtinicnu 2022-09-07

Solve the following system in $R$ :
${\begin{cases} \frac{y}{x} + \frac{x}{y} = \frac{17}{4} \\ x^{2} - y^{2} = 25 \end{cases}$

calcific5z 2022-09-07

Solving simultaneous equations with `min{}` function
x1=min{a+bx2, c};
x2=min{a+bx3, c};
.
.
.
xm=min{a+b*x1, c};

engausidarb 2022-09-07

Every $3 \times 3$ skew symmetric matrix is singular. Because this is a skew symmetric matrix, $det (A) = det (A^{T}) = det (- A) = (- 1)^{n} det (A)$ , and when $n$ is odd $det (A) = - det (A)$ , so $2 det (A) = 0$ and therefore $det (A) = 0$ . As such, the answer is "False" because it is only singular when n is odd.

In simple terms, systems of equations represent a special set of simultaneous equations where the equation system is used as a finite element. The trick here is to find common solutions, which is exactly what systems of equations solver must achieve. If this does not sound clear to you, take a look at some systems of equations answers below and see those with explanations. The solution will always come in three variables (namely, x, y, and z), which will represent your ordered triple. See systems of equations solutions for more examples of how it works in practice.

Algebra I

Strengthen Your Systems of Equations Skills