# 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... 154 views 1 answers 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 views 1 answers Solve $$3x^2+5x+2x-1=0$$ 154 views 1 answers Simplify $$3x^2+5x+2x-1=0$$ 339 views 1 answers What is a perceptual map? 461 views 1 answers How do I solve linear inequalities? 632 views 1 answers What are linear mixed models in SPSS? 227 views 1 answers Solve for x in x – 2 + 3 = –5. Show all steps 234 views 1 answers Solve for $$x$$ in $$\frac{2 x}{3}=12$$ 238 views 1 answers Solve the equation $$x-5=25$$ 276 views 1 answers state theory of "VC (Vapnik-Chervonenkis) dimension 180 views 1 answers What is the slope-intercept form of a linear equation? 251 views 0 answers how to graph linear equations 476 views 1 answers Solve the equation: $$2(x + 3) = 12$$ 248 views 1 answers Is time linear? 339 views 1 answers How do businesses use linear programming to optimize resources and maximize profit? 748 views 1 answers 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... 731 views 1 answers How do you fit a linear model in R? 251 views 0 answers 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 $$|A|=-1$$(... 402 views 1 answers What does a linear regression model look like? 393 views 1 answers What are linear equations? 493 views 0 answers What is the difference between a linear and non-linear function? 346 views 0 answers Prove that the equation $$x^2+y^2+z^2=x+y+z+1$$ has no rational solutions. 271 views 0 answers 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... 250 views 0 answers 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... 371 views 1 answers Where can I get free linear algebra notes? 868 views 1 answers What is the main objective of linear algebra? 305 views 1 answers Consider a linear operator \(L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$$,$L\left(\begin{array}{l}x \\y\end{array}\right)=\left(\begin{array}{ll}1 & 1 \\0 & 1\end{arra... 309 views 1 answers What is a matrix transformation in mathematics? 484 views 1 answers What is a linear transformation in mathematics? 963 views 1 answers Let $$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 ...
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...
Prove that the equation $$x^{6}+x^{4}+2 x^{2}+1=0$$ has no real solutions.