# Recent questions tagged theorem

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Let $\mathcal{P}_{3}$ be the space of polynomials of degree at most 3 anD let $D: \mathcal{P}_{3} \rightarrow \mathcal{P}_{3}$ be the derivative operator.
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Let $\mathcal{P}_{3}$ be the space of polynomials of degree at most 3 anD let $D: \mathcal{P}_{3} \rightarrow \mathcal{P}_{3}$ be the derivative operator.Let $\mathcal{P}_{3}$ be the space of polynomials of degree at most 3 anD let $D: \mathcal{P}_{3} \rightarrow \mathcal{P}_{3}$ be the derivative o ...
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Let $\mathcal{P}_{2}$ be the space of polynomials of degree at most 2 .
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Let $\mathcal{P}_{2}$ be the space of polynomials of degree at most 2 .Let $\mathcal{P}_{2}$ be the space of polynomials of degree at most 2 . &nbsp; a) Find a basis for this space. b) Let $D: \mathcal{P}_{2} \righta ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \(\mathcal{P}_{1}$ be the linear space of real polynomials of degree at most one, so a typical element is $p(x):=a+b x$, where $a$ and $b$ are real numbers.
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Let $\mathcal{P}_{1}$ be the linear space of real polynomials of degree at most one, so a typical element is $p(x):=a+b x$, where $a$ and $b$ are real numbers.Let $\mathcal{P}_{1}$ be the linear space of real polynomials of degree at most one, so a typical element is $p(x):=a+b x$, where $a$ and $b$ ...
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Let $A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}$ be a linear map. Show that the following are equivalent.
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Let $A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}$ be a linear map. Show that the following are equivalent.Let $A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}$ be a linear map. Show that the following are equivalent. a) For every $y \in \mathbb{R}^{k}$ th ...
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Let $\mathcal{P}_{k}$ be the space of polynomials of degree at most $k$ and define the linear map $L: \mathcal{P}_{k} \rightarrow \mathcal{P}_{k+1}$ by $L p:=p^{\prime \prime}(x)+x p(x) .$Let $\mathcal{P}_{k}$ be the space of polynomials of degree at most $k$ and define the linear map $L: \mathcal{P}_{k} \rightarrow \mathcal{P}_{k+ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The five-digit number 1234A is divisible by 9. What is the remainder when it is divided by 7 ? 0 answers 6 views The five-digit number 1234A is divisible by 9. What is the remainder when it is divided by 7 ?The five-digit number 1234A is divisible by 9. What is the remainder when it is divided by 7 ? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is there to know about the Binomial Coefficients and the Binomial Theorem? 1 answer 12 views What is there to know about the Binomial Coefficients and the Binomial Theorem?What is there to know about the Binomial Coefficients and the Binomial Theorem? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove the orthogonal projection theorem 1 answer 4 views Prove the orthogonal projection theoremProve the orthogonal projection theorem ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What does the Theorem of Pythagoras in R^n state? 1 answer 6 views What does the Theorem of Pythagoras in R^n state?What does the Theorem of Pythagoras in R^n state? ... close 1 answer 7 views If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that  \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that  \|\mathbf{u}+\mathbf{v}\|^{2}= ... close 0 answers 7 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 State the Binomial Theorem. 0 answers 3 views State the Binomial Theorem.State the Binomial Theorem. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 De Moivre's Theorem gives \cos 3 \theta as: 0 answers 5 views De Moivre's Theorem gives \cos 3 \theta as:De Moivre's Theorem gives \cos 3 \theta as: ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The Mean Value Theorem does not apply to 0 answers 5 views The Mean Value Theorem does not apply toThe Mean Value Theorem does not apply to &nbsp; A. f(x)=\frac{x}{x^{2}-4} on 0,1, B. f(x)=\frac{x}{x^{2}+4} on 0,1, C. f(x)=\frac{\sq ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 State Rolle's Theorem. 0 answers 3 views State Rolle's Theorem.State Rolle's Theorem. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove Rolle's Theorem under the assumption that for the function f on [a, b] you have f(x)>f(a) for some x in the domain of f. 0 answers 5 views Prove Rolle's Theorem under the assumption that for the function f on [a, b] you have f(x)>f(a) for some x in the domain of f.Prove Rolle's Theorem under the assumption that for the function f on a, b you have f(x)&gt;f(a) for some x in the domain of f. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the domain, the asymptotes (if any) of f and classify each asymptote as vertical, horizontal or slant. 0 answers 5 views Find the domain, the asymptotes (if any) of f and classify each asymptote as vertical, horizontal or slant.Let  f(x)=\frac{x^{2}-3}{x+2}  You may use that  f^{\prime}(x)=\frac{x^{2}+4 x+3}{(x+2)^{2}} \quad \text { and } \quad f^{\prime \prime}(x)=\fra ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 State the remainder theorem of polynomials 1 answer 6 views State the remainder theorem of polynomialsState the remainder theorem of polynomials ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove the remainder theorem of polynomials 1 answer 8 views Prove the remainder theorem of polynomialsProve the remainder theorem of polynomials ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Use the remainder theorem to factorize the following: 0 answers 3 views Use the remainder theorem to factorize the following: Use the remainder theorem to factorise the following: \(a(x)=x^{3}-7 x+6$ $a(x)=x^{6}-6 x^{4}+9 x^{2}-4$ ...
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What is the fundamental theorem of algebra?
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What is the fundamental theorem of algebra?What is the fundamental theorem of algebra? ...
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Use the Remainder Theorem to find linear factors for the polynomials below. Once you are down to a quadratic, you can use the quadratic formula instead.
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Use the Remainder Theorem to find linear factors for the polynomials below. Once you are down to a quadratic, you can use the quadratic formula instead.Use the Remainder Theorem to find linear factors for the polynomials below. Once you are down to a quadratic, you can use the quadratic formula instea ...
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Use double angle formulae to prove the identities
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Use double angle formulae to prove the identitiesUse double angle formulae to prove the identities \ \sin 2 A=\frac{2 \tan A}{1+\tan ^{2} A}, \quad \cos 2 A=\frac{1-\tan ^{2} A}{1+\tan ^{2} A}, \qua ...
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Is algebra easier than calculus?
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Is algebra easier than calculus?Is algebra easier than calculus? ...
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Define the Discrete-Time Fourier transform - Parseval's Theorem
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Define the Discrete-Time Fourier transform - Parseval's TheoremDefine the Discrete-Time Fourier transform - Parseval's Theorem ...
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