# Recent questions tagged vectors

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$-\frac{3}{4}$ is a root of the equation $0=12 y^{2}-7 y+c$. Determine the value of $c$ and the other root.
$-\frac{3}{4}$ is a root of the equation $0=12 y^{2}-7 y+c$. Determine the value of $c$ and the other root.$-\frac{3}{4}$ is a root of the equation $0=12 y^{2}-7 y+c$. Determine the value of $c$ and the other root. ...
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Solve for the variables simultaneously: \begin{array}{l} 2 y-x=5 \\ 3 x+2 y-10=0 \end{array}
Solve for the variables simultaneously: \begin{array}{l} 2 y-x=5 \\ 3 x+2 y-10=0 \end{array}Solve for the variables simultaneously: \begin{array}{l} 2 y-x=5 \\ 3 x+2 y-10=0 \end{array} ...
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The points A, B and $\mathrm{C}$ have position vectors
The points A, B and $\mathrm{C}$ have position vectorsThe points A, B and $\mathrm{C}$ have position vectors $\boldsymbol{a}=i-3 j, \quad \boldsymbol{b}=2 i-j+k$ and $\boldsymbol{c}=10 j+10 k$ respectivel ...
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Prove that the following vectors are non-coplanar
Prove that the following vectors are non-coplanar Prove that the following vectors are non-coplanar: $3 \hat{i}+ \hat{j}- \hat{k}$ ,$\quad 2 \hat{i}- \hat{j}+7 \hat{k}$ and $7 \hat{ i}- \hat{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given:$f(x)=2 x^{3}-2 x^{2}+4 x-1$. Determine the interval on which$f$is concave Up. 1 answer 48 views Given:$f(x)=2 x^{3}-2 x^{2}+4 x-1$. Determine the interval on which$f$is concave Up.Given:$f(x)=2 x^{3}-2 x^{2}+4 x-1$. Determine the interval on which$f$is concave Up. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the values of$A$and$B$0 answers 47 views Find the values of$A$and$B$Find the values of$A$and$B$that make $$f(x)=\left\{\begin{array}{lll} x^{2}+1 &amp; \text { if } &amp; x \geq 0 \\ A \sin x+B \cos x &amp; \text ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If the eigenvalues of \mathbf{A} are 100,-50,3 \pm 5 \sqrt{-1}, then find a lower bound on cond (\mathbf{A}) 1 answer 54 views If the eigenvalues of \mathbf{A} are 100,-50,3 \pm 5 \sqrt{-1}, then find a lower bound on cond (\mathbf{A}) Given a nonsingular n \times n matrix \mathbf{A}, and n \times 1 vectors \mathbf{x}, \hat{\mathbf{x}}, \mathbf{b}=\mathbf{A x}, and \hat{\mat ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a better bound for$$ \frac{\|\mathbf{x}-\hat{\mathbf{x}}\|}{\|\mathbf{x}\|} \times \frac{\|\mathbf{b}\|}{\|\mathbf{b}-\hat{\mathbf{b}}\|} $$1 answer 36 views Find a better bound for$$ \frac{\|\mathbf{x}-\hat{\mathbf{x}}\|}{\|\mathbf{x}\|} \times \frac{\|\mathbf{b}\|}{\|\mathbf{b}-\hat{\mathbf{b}}\|} $$Given a nonsingular n \times n matrix \mathbf{A}, and n \times 1 vectors \mathbf{x}, \hat{\mathbf{x}}, \mathbf{b}=\mathbf{A x}, and \hat{\mat ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Calculate the norm of the vectors 0 answers 21 views Calculate the norm of the vectors \(Let \ \bar{a} = \begin{pmatrix}2\\-1\end{pmatrix} \ and \ \bar{b} = \begin{pmatrix}-3\\4\end{pmatrix} \\ a) \ Calculate \ the \ norm \ of \ \bar{a ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given that$$ G=\left[\begin{array}{lll} 2 & 5 & 4 \\ 3 & 1 & 2 \\ 5 & 4 & 6 \end{array}\right] $$compute 1 answer 82 views Given that$$ G=\left[\begin{array}{lll} 2 & 5 & 4 \\ 3 & 1 & 2 \\ 5 & 4 & 6 \end{array}\right] $$compute(a) Given that$$ G=\left\begin{array}{lll} 2 &amp; 5 &amp; 4 \\ 3 &amp; 1 &amp; 2 \\ 5 &amp; 4 &amp; 6 \end{array}\right $$compute \operatorname{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determıne an equation for the plane that passes through the point (1,1,1) and is parallel to the plane$$ x-3 y-2 z-4=0 $$0 answers 78 views Determıne an equation for the plane that passes through the point (1,1,1) and is parallel to the plane$$ x-3 y-2 z-4=0 $$1. Determıne an equation for the plane that passes through the point (1,1,1) and is parallel to the plane$$ x-3 y-2 z-4=0$$2. Determine the volum ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that if A is positive semi-definite and$\epsilon>0$, then$\mathbf{A}+\epsilon \mathbf{I}$is positive definite. 1 answer 65 views Prove that if A is positive semi-definite and$\epsilon>0$, then$\mathbf{A}+\epsilon \mathbf{I}$is positive definite.Prove that if A is positive semi-definite and$\epsilon&gt;0$, then$\mathbf{A}+\epsilon \mathbf{I}$is positive definite. ... close 1 answer 63 views Prove that for$\mathbf{A} \in \mathbb{R}^{m \times n}$,$\mathbf{A}^{\top} \mathbf{A}$is positive semi-definite. If$\operatorname{null}(\mathbf{A})=\{0\}$, then$\mathbf{A}^{\top} \mathbf{A}$is positive definite.Prove that for &nbsp;$\mathbf{A} \in \mathbb{R}^{m \times n}$,$\mathbf{A}^{\top} \mathbf{A}$is positive semi-definite. If$\operatorname{null}(\math ...
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A symmetric matrix A is positive semi-definite if
A symmetric matrix A is positive semi-definite ifA symmetric matrix A is positive semi-definite if ...
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What are the properties of Rayleigh quotients?
What are the properties of Rayleigh quotients?What are the properties of Rayleigh quotients? ...
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A matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric if
A matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric ifA matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric if ...
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A matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal if
A matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal ifA matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal if ...
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Let $\mathbf{x}$ be an eigenvector of $\mathbf{A}$ with corresponding eigenvalue $\lambda$. Then
Let $\mathbf{x}$ be an eigenvector of $\mathbf{A}$ with corresponding eigenvalue $\lambda$. ThenLet $\mathbf{x}$ be an eigenvector of $\mathbf{A}$ with corresponding eigenvalue $\lambda$. Then ...
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We say that a nonzero vector $\mathrm{x} \in \mathbb{R}^{n}$ is an eigenvector of A corresponding to eigenvalue $\lambda$ if
We say that a nonzero vector $\mathrm{x} \in \mathbb{R}^{n}$ is an eigenvector of A corresponding to eigenvalue $\lambda$ ifFor a square matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$, there may be vectors which, when $\mathbf{A}$ is applied to them, are simply scaled by s ...
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What are the algebraic properties of the Transpose in matrices and vectors?
What are the algebraic properties of the Transpose in matrices and vectors?What are the algebraic properties of the Transpose in matrices and vectors? ...
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Find the projection of $u = <3,-12>$ onto $v = <9,2>$
Find the projection of $u = <3,-12>$ onto $v = <9,2>$Find the projection of $u = &lt;3,-12&gt;$ onto $v = &lt;9,2&gt;$ ...
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Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?
Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?Find the dot product of $u = &lt;-5,-6,-2&gt;$ and $v = &lt;-3,10,8&gt;$. Are $u$ and $v$ orthogonal? ...
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What are the basic principle of vectors and scalars?