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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.
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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
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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 ...
by MathsGee Platinum
(102,806 points)
asked in Mathematics May 19, 2021
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Prove that the following vectors are non-coplanar
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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{ ...
by MathsGee Platinum
(102,806 points)
asked in Mathematics May 14, 2021
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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
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Find the values of $A$ and $B$
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Find the values of $A$ and $B$Find the values of $A$ and $B$ that make $$ f(x)=\left\{\begin{array}{lll} x^{2}+1 & \text { if } & x \geq 0 \\ A \sin x+B \cos x & \text ...
by MathsGee Platinum
(102,806 points)
asked in Mathematics May 10, 2021
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If the eigenvalues of $\mathbf{A}$ are $100,-50,3 \pm 5 \sqrt{-1}$, then find a lower bound on cond $(\mathbf{A})$ 
1 answer 54 views
If the eigenvalues of $\mathbf{A}$ are $100,-50,3 \pm 5 \sqrt{-1}$, then find a lower bound on cond $(\mathbf{A})$ Given a nonsingular $n \times n$ matrix $\mathbf{A}$, and $n \times 1$ vectors $\mathbf{x}, \hat{\mathbf{x}}, \mathbf{b}=\mathbf{A x}$, and $\hat{\mat ...
by MathsGee Platinum
(102,806 points)
asked in Mathematics May 9, 2021
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Find a better bound for $$ \frac{\|\mathbf{x}-\hat{\mathbf{x}}\|}{\|\mathbf{x}\|} \times \frac{\|\mathbf{b}\|}{\|\mathbf{b}-\hat{\mathbf{b}}\|} $$

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Calculate the norm of the vectors
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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 ...
by Claudia Wooden
(4,756 points)
asked in Mathematics May 9, 2021
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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 $$ G=\left\begin{array}{lll} 2 & 5 & 4 \\ 3 & 1 & 2 \\ 5 & 4 & 6 \end{array}\right $$ compute $\operatorname{ ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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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 ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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Prove that if A is positive semi-definite and $\epsilon>0$, then $\mathbf{A}+\epsilon \mathbf{I}$ is positive definite.
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A symmetric matrix A is positive semi-definite if
1 answer 110 views
A symmetric matrix A is positive semi-definite ifA symmetric matrix A is positive semi-definite if ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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What are the properties of Rayleigh quotients?
1 answer 64 views
What are the properties of Rayleigh quotients?What are the properties of Rayleigh quotients? ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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A matrix $\mathbf{A} \in \mathbb{R}^{n \times n}$ is said to be symmetric if
1 answer 75 views
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 ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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A matrix $\mathbf{Q} \in \mathbb{R}^{n \times n}$ is said to be orthogonal if
1 answer 64 views
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 ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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Let $\mathbf{x}$ 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
1 answer 72 views
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 ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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What are the algebraic properties of the Transpose in matrices and vectors?
1 answer 55 views
What are the algebraic properties of the Transpose in matrices and vectors?What are the algebraic properties of the Transpose in matrices and vectors? ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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Find the projection of $u = <3,-12>$ onto $v = <9,2>$
0 answers 68 views
Find the projection of $u = <3,-12>$ onto $v = <9,2>$Find the projection of $u = &lt;3,-12&gt;$ onto $v = &lt;9,2&gt;$ ...
by MathsGee Platinum
(102,806 points)
asked in Mathematics Apr 12, 2021
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Find the dot product of $u = <-5,-6,-2>$ and $v = <-3,10,8>$. Are $u$ and $v$ orthogonal?
0 answers 89 views
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? ...
by MathsGee Platinum
(102,806 points)
asked in Mathematics Apr 12, 2021
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What are the basic principle of vectors and scalars?
1 answer 83 views
What are the basic principle of vectors and scalars?What are the basic principle of vectors and scalars? ...
by Eddie Wooden
(2,002 points)
asked in Physics Mar 29, 2021
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An object subject only to gravity is
1 answer 83 views
An object subject only to gravity isAn object subject only to gravity is ...
by MathsGee Platinum
(102,806 points)
asked in Physics Mar 28, 2021
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