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What is a column matrix in mathematics?

asked Jan 10 by ♦MathsGee Diamond (89,175 points) | 72 views

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What is a row matrix in mathematics?

asked Jan 10 by ♦MathsGee Diamond (89,175 points) | 66 views

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How many possibilities are there to distribute 15 letters among 5 people so that each of them receives at least one letter?

asked Nov 27, 2022 by ♦MathsGee Diamond (89,175 points) | 73 views

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An absent-minded mathematician writes \(n\) letters and seals the envelopes before writing the addresses on the envelopes. Hence he randomly writes the addresses on the envelopes.

asked Nov 27, 2022 by ♦MathsGee Diamond (89,175 points) | 68 views

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Nine journalists, each from a different country, participates in a press conference. None of them can speak more than three languages, and each two journalists have at least one common language.

asked Sep 22, 2022 by ♦MathsGee Diamond (89,175 points) | 82 views

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Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter.

asked Jul 28, 2022 by ♦MathsGee Diamond (89,175 points) | 103 views

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\(S T U R\) is a parallelogram, with \(S U X, T U W\) and \(R U V\) straight lines. Prove \(R T \| V W\).

asked Apr 17, 2022 by ♦GaussTheBot Diamond (45,615 points) | 175 views

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Sketch the curve \[ x=\sin ^{2} \pi t, y=\cos ^{2} \pi t, 0 \leq t \leq 2 . \]

asked Feb 4, 2022 by ♦GaussTheBot Diamond (45,615 points) | 245 views

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The components of the vector $\mathbf{v}=\overrightarrow{P_{1} P_{2}}$ with initial point $P_{1}(2,-1,4)$ and terminal point $P_{2}(7,5,-8)$ are

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 171 views

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If $\mathbf{v}=(1,-3,2)$ and $\mathbf{w}=(4,2,1)$, then

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 274 views

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Prove that if $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ are vectors in $R^{n}$, and if $k$ and $m$ are scalars, then:

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 413 views

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Prove that If $\mathbf{v}$ is a vector in $R^{n}$ and $k$ is a scalar, then:

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 408 views

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Find the components of the vector $\overrightarrow{P_{1} P_{2}}$ when $P_1(3,5)$ and $P_2(2,8)$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 138 views

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Find the components of the vector $\overrightarrow{P_{1} P_{2}}$ when $P_1(-6,2)$ and $P_2(-4,-1)$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 150 views

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Find the components of the vector $\overrightarrow{P_{1} P_{2}}$ when $P_1(0,0,0)$ and $P_2(-1,6,1)$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 151 views

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Find the terminal point of the vector that is equivalent to $\mathbf{u}=(1,2)$ and whose initial point is $A(1,1)$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 290 views

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Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,1,3)$ and whose terminal point is $B(-1,-1,2)$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 168 views

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Find the initial point of the vector that is equivalent to $\mathbf{u}=(1,2)$ and whose terminal point is $B(2,0)$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 194 views

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Find an initial point $P$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with terminal point $Q(3,0,-5)$ and such that $\mathbb{u}$ has the same direction as $\mathbf{v}=(4,-2,-1)$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 203 views

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Let $\mathbf{u}=(4,-1), \mathbf{v}=(0,5)$, and $\mathbf{w}=(-3,-3)$. Find the components of

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 324 views

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Find a terminal point $Q$ of a nonzero vector $\mathbf{u}=\overrightarrow{P Q}$ with initial point $P(-1,3,-5)$ and such that

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 171 views

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Let $\mathbf{u}=(-3,1,2), \mathbf{v}=(4,0,-8)$, and $\mathbf{w}=(6,-1,-4)$. Find the components of

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 319 views

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Which of the following vectors in $R^{6}$, if any, are parallel to $\mathbf{u}=(-2,1,0,3,5,1) ?$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 237 views

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For what value(s) of $t$, if any, is the given vector parallel to $\mathbf{u}=(4,-1)$ ?

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 305 views

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Let $\mathbf{u}=(1,-1,3,5)$ and $\mathbf{v}=(2,1,0,-3)$. Find scalars $a$ and $b$ so that $a \mathbf{u}+b \mathbf{v}=(1,-4,9,18)$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 281 views

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Find scalars $c_{1}, c_{2}$, and $c_{3}$ for which the equation is satisfied.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 144 views

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Show that there do not exist scalars $c_{1}, c_{2}$, and $c_{3}$ such that $$ c_{1}(-2,9,6)+c_{2}(-3,2,1)+c_{3}(1,7,5)=(0,5,4) $$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 184 views

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Show that there do not exist scalars $c_{1}, c_{2}$, and $c_{3}$ such that $c_{1}(1,0,1,0)+c_{2}(1,0,-2,1)+c_{3}(2,0,1,2)=(1,-2,2,3)$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 165 views

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In relation to the points $P_{1}$ and $P_{2}$, what can you say about the terminal point of the following vector if its initial point is at the origin?

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 116 views

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If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 191 views

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True/False: If $k$ is a scalar and $\mathbf{v}$ is a vector, then $\mathbf{v}$ and $k \mathbf{v}$ are parallel if and only if $k \geq 0$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 347 views

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True/False: The vectors $\mathbf{v}+(\mathbf{u}+\mathbf{w})$ and $(\mathbf{w}+\mathbf{v})+\mathbf{u}$ are the same.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 390 views

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True/False: If $\mathbf{u}+\mathbf{v}=\mathbf{u}+\mathbf{w}$, then $\mathbf{v}=\mathbf{w}$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 353 views

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True/False: If $(a, b, c)+(x, y, z)=(x, y, z)$, then $(a, b, c)$ must be the zero vector.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 370 views

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True/False: If $k$ and $m$ are scalars and $\mathbf{u}$ and $\mathbf{v}$ are vectors, then $$ (k+m)(\mathbf{u}+\mathbf{v})=k \mathbf{u}+m \mathbf{v} $$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 433 views

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True/False: If the vectors $\mathbf{v}$ and $\mathbf{w}$ are given, then the vector equation

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 342 views

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True/False: The linear combinations $a_{1} \mathbf{v}_{1}+a_{2} \mathbf{v}_{2}$ and $b_{1} \mathbf{v}_{1}+b_{2} \mathbf{v}_{2}$ can only be equal if $a_{1}=b_{1}$ and $a_{2}=b_{2}$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 341 views

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What is the norm of the vector $\mathbf{v}=(-3,2,1)$ in $R^{3}$?

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 308 views

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What is the norm of the vector $\mathbf{v}=(2,-1,3,-5)$ in $R^{4}$?

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 181 views

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Show that $\mathbf{u}=\frac{1}{\|\mathbf{v}\|} \mathbf{v}$ is a unit vector

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 235 views

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Find the unit vector $\mathbf{u}$ that has the same direction as $\mathbf{v}=(2,2,-1)$.

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 135 views

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Prove that if $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ are vectors in $R^{n}$, and if $k$ is a scalar, then $(\mathbf{u}+\mathbf{v}) \cdot \mathbf{w}=\mathbf{u} \cdot \mathbf{w}+\mathbf{v} \cdot \mathbf{w}$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 390 views

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What is the dot product $(\mathbf{u}-2 \mathbf{v}) \cdot(3 \mathbf{u}+4 \mathbf{v})$

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 277 views

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Prove that if $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ are vectors in $R^{n}$, then:

asked Jan 26, 2022 by ♦MathsGee Diamond (89,175 points) | 431 views

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Show that both \(A^{*} A\) and \(A A^{*}\) are self-adjoint.

asked Jan 21, 2022 by ♦MathsGee Diamond (89,175 points) | 128 views

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Answer the following in terms of \(\mathbf{V}, \mathbf{W}\), and \(\mathbf{Z}\).

asked Jan 21, 2022 by ♦MathsGee Diamond (89,175 points) | 145 views

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What is the dot product of u a row matrix and v a column matrix?

asked Jan 13, 2022 by ♦MathsGee Diamond (89,175 points) | 245 views

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What is the dot product of u a column matrix and v a row matrix?

asked Jan 13, 2022 by ♦MathsGee Diamond (89,175 points) | 262 views

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Let $\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$ be a fixed vector in $R^{2}$. In each part, describe in words the set of all vectors $\mathbf{r}=(x, y)$ that satisfy the stated condition.

asked Jan 13, 2022 by ♦MathsGee Diamond (89,175 points) | 425 views

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Find the norm of $v$, and a unit vector that is oppositely directed to $\mathbf{v} = (1, -1, 2)$

asked Jan 13, 2022 by ♦MathsGee Diamond (89,175 points) | 284 views

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