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If \(A\) and \(B\) are \(4 \times 4\) matrices such that \(\operatorname{rank}(A B)=3\), then \(\operatorname{rank}(B A)<4\).
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If \(A\) and \(B\) are \(4 \times 4\) matrices such that \(\operatorname{rank}(A B)=3\), then \(\operatorname{rank}(B A)<4\).For each of the following, answer TRUE or FALSE. If the statement is false in even a single instance, then the answer is FALSE. There is no need to ju ...
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Consider the system of linear equations
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Consider the system of linear equationsConsider the system of linear equations \ \begin{array}{rc} k x+y+z &amp; =1 \\ x+k y+z &amp; =1 \\ x+y+k z &amp; =1 \end{array} \ For what value(s) ...
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asked in Mathematics 9 hours ago
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Solve the equations for \(x, y\), and \(z\).
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Solve the equations for \(x, y\), and \(z\).Solve the equations for \(x, y\), and \(z\). \(x+0 y+3 z=2 \) \(2 x+3 y+2 z=1\) \(2 x+2 y+3 z=3\) HINT: If \(A=\left(\begin{array}{lll}2 &amp; 3 & ...
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asked in Mathematics 9 hours ago
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Consider the system of equations \[ \begin{aligned} &x+y-z=a \\ &x-y+2 z=b . \end{aligned} \]
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Consider the system of equations \[ \begin{aligned} &x+y-z=a \\ &x-y+2 z=b . \end{aligned} \]Consider the system of equations \ \begin{aligned} &amp;x+y-z=a \\ &amp;x-y+2 z=b . \end{aligned} \ a) Find the general solution of the homogeneous ...
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asked in Mathematics 9 hours ago
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Solve the given system - or show that no solution exists:
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Solve the given system - or show that no solution exists:Solve the given system - or show that no solution exists: \ \begin{aligned} x+2 y &amp;=&amp; 1 \\ 3 x+2 y+&amp; 4 z=&amp; 7 \\ -2 x+y-&amp; 2 z=&am ...
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asked in Mathematics 12 hours ago
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Which of the following sets are linear spaces?
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Which of the following sets are linear spaces?Which of the following sets are linear spaces? a) \(\left\{X=\left(x_{1}, x_{2}, x_{3}\right)\right.\) in \(\mathbb{R}^{3}\) with the property \(\lef ...
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asked in Mathematics 13 hours ago
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Interactive Video: How well do you know the London Map System?
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Interactive Video: How well do you know the London Map System? Interactive Video: How well do you know the London Map System? &nbsp; &nbsp; ...
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asked in General Knowledge 1 day ago
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Which of the following operations over a system of linear equations could change the solution set?
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Which of the following operations over a system of linear equations could change the solution set?Which of the following operations over a system of linear equations could change the solution set? A) interchanging two equations B) removing an equ ...
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asked in Mathematics Jan 13
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Which of the following is the direction vector of the line $$ \left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right. $$

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Calculate the determinant $$ \left|\begin{array}{rrrr} 4 & 2 & 3 & 4 \\ 1 & 0 & 1 & 2 \\ 1 & -1 & 1 & 0 \\ 5 & 1 & 4 & 3 \end{array}\right| $$

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Which of the following is the coefficient matrix for the system  \begin{array}{c} x+4 y=6 \\ 4 x+2 y=z \text { ? } \\ y+5 z=-6 \end{array}
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Which of the following is the direction vector of the line $$ \left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right. $$
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Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$
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Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$Which of the following is the equation of the plane through the points $(3,-2,5),(1,4,-1),(2,-6,7) ?$ \begin{equation} \text { A. }\left|\begin{array} ...
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asked in Mathematics Jan 13
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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}, \times$ denotes the cross product, . the dot product. Which of the following is false?
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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}$, such that $a \cdot(b \times c)=0$. Then
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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}$, such that $a \cdot(b \times c)=0$. ThenLet $a, b$ and $c$ be vectors in $\mathrm{R}^{3}$, such that $a \cdot(b \times c)=0$. Then A. $a, b$ and $c$ are colinear B. $a, b$ and $c$ lie on t ...
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asked in Mathematics Jan 13
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Which of the following is the equation of the plane which passes through the point $A(-3,4,-3)$ and contains the line $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$

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Interpret the solution of the given system of equations geometrically on the diagram:
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Interpret the solution of the given system of equations geometrically on the diagram: Interpret the solution of the given system of equations geometrically on the diagram: $$ \begin{gathered} 3 x-6 y+9 z=3 \\ 2 x-3 y+5 z=7 \\ 2 ...
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asked in Mathematics Jan 13
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Let $\vec{a}$ and $\vec{b}$ be non-zero, non parallel vectors. Identify proj $\vec{a} \vec{b}$ geometrically in the diagram.
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Which of the following operations over a system of linear equations changes the solution set?
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Which of the following operations over a system of linear equations changes the solution set?Which of the following operations over a system of linear equations changes the solution set? &nbsp; A) interchanging two equations B) multiplying ...
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asked in Mathematics Jan 13
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Which of the following is the direction vector of the line
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Which of the following is the direction vector of the lineWhich of the following is the direction vector of the line $$ \left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right. $$ ...
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asked in Mathematics Jan 13
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Solve the system $$ \begin{gathered} 4 x_{1}+2 x_{3}=4 \\ 3 x_{1}-2 x_{4}=0 \\ 2 x_{1}+x_{2}+x_{4}=1 \end{gathered} $$
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Calculate the determinant $$ \left|\begin{array}{rrrr} -2 & 1 & -1 & 1 \\ 3 & 2 & 0 & -4 \\ -1 & 1 & 2 & -1 \\ 1 & -1 & 3 & -2 \end{array}\right| $$

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Write the equation of the plane through the points $ (3,-2,5),(1,4,-1),(2,-6,7) $
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Which of the following calculations is wrong?
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Which of the following calculations is wrong?Which of the following calculations is wrong? &nbsp; A. $\lim _{x \rightarrow \infty} \dfrac{e^{x}}{x}=\lim _{x \rightarrow \infty} \dfrac{e^{x}}{1} ...
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asked in Mathematics Jan 13
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