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Topics
Pre-Algebra
Mean
Mode
Greatest Common Factor
Least Common Multiple
Order of Operations
Fractions
Mixed Fractions
Prime Factorization
Exponents
Radicals
Algebra
Combine Like Terms
Solve for a Variable
Factor
Expand
Evaluate Fractions
Linear Equations
Quadratic Equations
Inequalities
Systems of Equations
Matrices
Trigonometry
Simplify
Evaluate
Graphs
Solve Equations
Calculus
Derivatives
Integrals
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Solve for A, C, B, a, b
b=C
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Complex Number
5 problems similar to:
\left. \begin{array} { l } { A ^ {C} = B }\\ { a = C }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.
Similar Problems from Web Search
Relationship between eigenvalues of A^TA and B=\left[\begin{array}{cc} 0 & A^T\\ A & 0\end{array}\right]
https://math.stackexchange.com/questions/2014959/relationship-between-eigenvalues-of-ata-and-b-left-beginarraycc-0-a
Since \mathrm A^{\top} \mathrm A is positive semidefinite, its eigenvalues, \mu_1, \dots, \mu_n, are nonnegative. The characteristic polynomial of \mathrm B is \det (s \mathrm I_{2n} - \mathrm B) = \det \begin{bmatrix} s \mathrm I_{n} & -\mathrm A^{\top}\\ -\mathrm A & s \mathrm I_{n} \end{bmatrix} = \det (s^2 \mathrm I_{n} - \mathrm A^{\top} \mathrm A) ...
Sufficient condition for the block matrix \big(\begin{smallmatrix} B & A^T \\ A & 0 \end{smallmatrix} \big) to be invertible
https://math.stackexchange.com/questions/1027138/sufficient-condition-for-the-block-matrix-big-beginsmallmatrix-b-at-a
Note that \ker A = {\cal R}Z. Suppose Bu + A^T v =0, Au = 0. Then u \in \ker A= {\cal R} Z, hence u = Zw for some w. Then Z^T B Zw + Z^T A^T v = Z^T B Zw + (AZ)^T v = Z^T B Zw = 0. Hence w=0 ...
Cholesky factor when adding a row and column to already factorized matrix
https://math.stackexchange.com/q/955874
To make this work, you should explicitly assume that a^tA^{-1}a<1; otherwise, the bordered matrix B:=\begin{bmatrix}A & a\\a^t & 1\end{bmatrix} would not be positive definite anymore (and ...
inverse of 2\times2 block matrix
https://math.stackexchange.com/q/1678502
One of the formulas here does not involve D^{-1}
Solve the Non-Homogeneous System y'=Cy+b(t)
https://math.stackexchange.com/q/2801318
Let V= \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} and note that C = V \begin{bmatrix} -1 & 0 \\ 0 & -3 \end{bmatrix} V^{-1} and so e^{Ct} = V \begin{bmatrix} e^{-t} & 0 \\ 0 & e^{-3t} \end{bmatrix} V^{-1} ...
Solving systems of ODE'S in the form \dot{\overrightarrow{u}}=A\overrightarrow{u}+\overrightarrow{b}
https://math.stackexchange.com/questions/2034180/solving-systems-of-odes-in-the-form-dot-overrightarrowu-a-overrightarrow
You can use the method of undetermined coefficients or educated guessing to find a particular solution. Since 0 is not an eigenvalue of A and \vec b is constant, look for a particular solution ...
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Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
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