# Recent questions tagged system

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If $A$ and $B$ are $4 \times 4$ matrices such that $\operatorname{rank}(A B)=3$, then $\operatorname{rank}(B A)<4$.
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
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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Solve the equations for $x, y$, and $z$.
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 & ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Consider the system of equations \begin{aligned} &x+y-z=a \\ &x-y+2 z=b . \end{aligned} 0 answers 4 views 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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the given system - or show that no solution exists: 0 answers 5 views 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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following sets are linear spaces? 0 answers 6 views 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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Interactive Video: How well do you know the London Map System?
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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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?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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Which of the following is the direction vector of the line $$\left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right.$$
Which of the following is the direction vector of the line $$\left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right.$$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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Solve the system $$\left\{\begin{array}{l} 4 x_{1}+2 x_{2}+3 x_{3}+4 x_{4}=0 \\ x_{1}+x_{3}+2 x_{4}=1 \\ x_{1}-x_{2}+x_{3}=1 \\ -3 x_{1}-2 x_{2}-2 x_{3}-2 x_{4}=1 \end{array}\right.$$Solve the system $$\left\{\begin{array}{l} 4 x_{1}+2 x_{2}+3 x_{3}+4 x_{4}=0 \\ x_{1}+x_{3}+2 x_{4}=1 \\ x_{1}-x_{2}+x_{3}=1 \\ -3 x_{1}-2 x_{2}-2 x_ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Calculate the determinant$$ \left|\begin{array}{rrrr} 4 & 2 & 3 & 4 \\ 1 & 0 & 1 & 2 \\ 1 & -1 & 1 & 0 \\ 5 & 1 & 4 & 3 \end{array}\right| $$0 answers 8 views Calculate the determinant$$ \left|\begin{array}{rrrr} 4 & 2 & 3 & 4 \\ 1 & 0 & 1 & 2 \\ 1 & -1 & 1 & 0 \\ 5 & 1 & 4 & 3 \end{array}\right| $$Calculate the determinant$$ \left|\begin{array}{rrrr} 4 &amp; 2 &amp; 3 &amp; 4 \\ 1 &amp; 0 &amp; 1 &amp; 2 \\ 1 &amp; -1 &amp; 1 &amp; 0 \\ 5 &amp; ...
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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}
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}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} A. $\left\b ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the direction vector of the line $$\left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right.$$ 0 answers 5 views Which of the following is the direction vector of the line $$\left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right.$$Which of the following is the direction vector of the line $$\left\{\begin{array}{l} -x=2+t \\ y=-1-t, t \in R \\ z=t \end{array}\right.$$ &nbsp; ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the equation of the plane through the points$(3,-2,5),(1,4,-1),(2,-6,7) ?$0 answers 7 views Which of the following is the equation of the plane through the points$(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) ?$\text { A. }\left|\begin{array} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false? 0 answers 7 views Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false?Let$a, b$and$c$be vectors in$\mathrm{R}^{3}, \times$denotes the cross product, . the dot product. Which of the following is false? A.$-a \time ...
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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}$, such that $a \cdot(b \times c)=0$. Then
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 ...
Which of the following is the equation of the plane which passes through the point $A(-3,4,-3)$ and contains the line $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$
Which of the following is the equation of the plane which passes through the point $A(-3,4,-3)$ and contains the line $v=(-1,3,-2)+t(-2,1,5), t \in \mathrm{R}$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 \m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Interpret the solution of the given system of equations geometrically on the diagram: 0 answers 2 views 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: $$\begin{gathered} 3 x-6 y+9 z=3 \\ 2 x-3 y+5 z=7 \\ 2 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \vec{a} and \vec{b} be non-zero, non parallel vectors. Identify proj \vec{a} \vec{b} geometrically in the diagram. 0 answers 4 views Let \vec{a} and \vec{b} be non-zero, non parallel vectors. Identify proj \vec{a} \vec{b} geometrically in the diagram. Let \vec{a} and \vec{b} be non-zero, non parallel vectors. Identify proj \vec{a} \vec{b} geometrically in the diagram. &nbsp; &nbsp; ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following operations over a system of linear equations changes the solution set? 0 answers 5 views Which of the following operations over a system of linear equations changes the solution set?Which of the following operations over a system of linear equations changes the solution set? &nbsp; A) interchanging two equations B) multiplying ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the direction vector of the line 0 answers 6 views Which of the following is the direction vector of the lineWhich of the following is the direction vector of the line$$ \left\{\begin{array}{l} x=2+t \\ y=-1-t, t \in \mathbb{R} \\ z=t \end{array}\right. $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the system$$ \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} $$0 answers 2 views Solve the system$$ \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} $$Solve the system$$ \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} $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Calculate the determinant$$ \left|\begin{array}{rrrr} -2 & 1 & -1 & 1 \\ 3 & 2 & 0 & -4 \\ -1 & 1 & 2 & -1 \\ 1 & -1 & 3 & -2 \end{array}\right| $$0 answers 7 views Calculate the determinant$$ \left|\begin{array}{rrrr} -2 & 1 & -1 & 1 \\ 3 & 2 & 0 & -4 \\ -1 & 1 & 2 & -1 \\ 1 & -1 & 3 & -2 \end{array}\right| $$Calculate the determinant$$ \left|\begin{array}{rrrr} -2 &amp; 1 &amp; -1 &amp; 1 \\ 3 &amp; 2 &amp; 0 &amp; -4 \\ -1 &amp; 1 &amp; 2 &amp; -1 \\ 1 & ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Write the equation of the plane through the points$ (3,-2,5),(1,4,-1),(2,-6,7) $0 answers 3 views Write the equation of the plane through the points$ (3,-2,5),(1,4,-1),(2,-6,7) $Write the equation of the plane through the points $$(3,-2,5),(1,4,-1),(2,-6,7)$$ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following calculations is wrong? 0 answers 4 views 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} ...