Recent questions tagged linear

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What is a linear transformation?
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Solve \(2(3x + 5) = -44\)
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Solve the linear equation \(4x+10=30\)
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Recall that for a matrix $A = (A_{ij})_{i,j=1}^n \in \mathbb{R}^{n\times n}$, and a vector $x = (x_1,...,x_n)^T \in \mathbb{R}^{n \times 1}$, matrix-vector multiplication...
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What are the most important concepts in linear algebra?
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Find the linear approximation to \( h(y)=\sin (y+1) \) at \( y=0 \). Use the linear approximation to approximate the value of \( \sin (2) \) and \( \sin (15) \). Compare ...
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Find the linear approximation to \( h(y)=\sin (y+1) \) at \( y=0 \). Use the linear approximation to approximate the value of \( \sin (2) \) and \( \sin (15) \). Compare ...
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Find a linear approximation to the function \( g(t)=\mathbf{e}^{\sin (t)} \) at \( t=-4 \)
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Find a linear approximation to the function \( g(x)=2-9 x-3 x^{2}-x^{3} \) at \( x=-1 \)
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Find a linear approximation to the function \( h(z)=\ln \left(z^{2}+5\right) \) at \( z=2 \)
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Find a linear approximation to the function \( f(x)=\cos (2 x) \) at \( x=\pi \)
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Find a linear approximation to \( h(t)=t^{4}-6 t^{3}+3 t-7 \) at \( t=-3 \).
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Find a linear approximation to the function \( f(x)=3 x \mathbf{e}^{2 x-10} \) at \( x=5 \) at the given point.
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Determine the linear approximation for \(\sin{\theta}\) at \(\theta = 0\) .
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Explain Bayesian model averaging (BMA) for linear regression
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How do you distinguish between "linear" and "non-linear" equations?
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Construct the simple linear regression equation of \( Y \) on \( X \) if\[\begin{array}{l}n=7, \sum_{i=1}^{n} x_{i}=113, \sum_{i=1}^{n} x_{i}^{2}=1983, \\\sum_{i=1}^{n} y...
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Consider four-wave mixing in a silicon waveguide and assume the crystallographic axes as your reference frame. Determine the polarization of the generated idler by consid...
161
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Solve \(3x^2+5x+2x-1=0\)
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Simplify \(3x^2+5x+2x-1=0\)
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What is a perceptual map?
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How do I solve linear inequalities?
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What are linear mixed models in SPSS?
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Solve for x in x – 2 + 3 = –5. Show all steps
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Solve for \(x\) in \(\frac{2 x}{3}=12\)
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Solve the equation \(x-5=25\)
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state theory of "VC (Vapnik-Chervonenkis) dimension
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What is the slope-intercept form of a linear equation?
251
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how to graph linear equations
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Solve the equation: \(2(x + 3) = 12\)
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Is time linear?
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How do businesses use linear programming to optimize resources and maximize profit?
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A company makes two products ( \(X\) and \(Y\) ) using two machines ( \(A\) and \(B\) ). Each unit of \(X\) that is produced requires 50 minutes processing time on machin...
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How do you fit a linear model in R?
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Let \(A\) be a \(2 \times 2\) real matrix with entries from \(\{0,1\}\) and \(|A| \neq 0\). Consider the following two statements :(P) If \(A \neq I_2\), then \(|A|=-1\)(...
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What does a linear regression model look like?
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What are linear equations?
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What is the difference between a linear and non-linear function?
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Prove that the equation \(x^2+y^2+z^2=x+y+z+1\) has no rational solutions.
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Given that \(z=3-3 \mathrm{i}\) express, in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are real numbers,(a) \(z^2\),(b) \(\frac{1}{z}\).(c) Find the exact value o...
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The complex numbers \(z_1\) and \(z_2\) are given by\[\begin{aligned}&z_1=5+3 \mathrm{i} \\&z_2=1+p \mathrm{i}\end{aligned}\]where \(p\) is an integer.(a) Find \(\frac{\m...
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Where can I get free linear algebra notes?
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What is the main objective of linear algebra?
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Consider a linear operator \(L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\),\[L\left(\begin{array}{l}x \\y\end{array}\right)=\left(\begin{array}{ll}1 & 1 \\0 & 1\end{arra...
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What is a matrix transformation in mathematics?
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What is a linear transformation in mathematics?
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Let \(T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}\) be the linear transformation defined by\[T(x, y, z)=(x+y+z, x+3 y+5 z)\]Let \(\beta\) and \(\gamma\) be the standard ...
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Let \(\beta\) and \(\gamma\) be the following standard ordered bases of \(M_{2 \times 2}(\mathbb{R})\) and \(P_{2}(\mathbb{R})\), respectively:\[\beta=\left\{\left(\begin...
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Let a: V -W be a linear map that is an endomorphism with bases B=(1,x2 ,x3) and defined by a (p)=(1- x2) . find the matrix A that represent the linear map ​​​​​...
228
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Prove that the equation \(x^{6}+x^{4}+2 x^{2}+1=0\) has no real solutions.
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