# Recent questions tagged matrices

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If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A}^{T} \mathbf{v}$
If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A}^{T} \mathbf{v}$If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A} ... close 0 answers 4 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The system of linear equations has $$\left\{\begin{array}{l} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{array}\right.$$ 0 answers 6 views The system of linear equations has $$\left\{\begin{array}{l} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{array}\right.$$The system of linear equations has $$\left\{\begin{array}{l} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{array}\right.$$ &nbsp; A) infinitely ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$A$and$B$be$n \times n$matrices. Which of the following is true? 0 answers 4 views Let$A$and$B$be$n \times n$matrices. Which of the following is true?Let$A$and$B$be$n \times n$matrices. Which of the following is true? &nbsp; A)$\operatorname{det}(A)=\operatorname{det}(-A)$B)$\operatornam ...
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Which of the following operations does not change the determinant?
If $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal to
If $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal toIf $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal to &nbsp; A) $(1,-4,-5)$ B) $(7,-4,5)$ C ...
Let $z_{1}=\left|z_{1}\right|\left(\cos \left(\theta_{1}\right)+i \sin \left(\theta_{1}\right)\right)$ and $z_{2}=\left|z_{2}\right|\left(\cos \left(\theta_{2}\right)+i \sin \left(\theta_{2}\right)\right)$ be two complex numbers.Let $z_{1}=\left|z_{1}\right|\left(\cos \left(\theta_{1}\right)+i \sin \left(\theta_{1}\right)\right)$ and z_{2}=\left|z_{2}\right|\left(\cos \left(\ ... close 0 answers 4 views 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 $$\left\{\begin{array}{l} 4 x_{1}+2 x_{2}+3 x_{3}+4 x_{4}=0 \\ x_{1}+x_{3}+2 x_{4}=1 \\ x_{1}-x_{2}+x_{3}=1 \\ -3 x_{1}-2 x_{2}-2 x_ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the inverse of the matrix$$ A=\left(\begin{array}{lll} 4 & 3 & 4 \\ 5 & 4 & 6 \\ 4 & 3 & 3 \end{array}\right) $$0 answers 3 views Find the inverse of the matrix$$ A=\left(\begin{array}{lll} 4 & 3 & 4 \\ 5 & 4 & 6 \\ 4 & 3 & 3 \end{array}\right) $$Find the inverse of the matrix$$ A=\left(\begin{array}{lll} 4 &amp; 3 &amp; 4 \\ 5 &amp; 4 &amp; 6 \\ 4 &amp; 3 &amp; 3 \end{array}\right) ... close 0 answers 4 views Which of the following systems has augmented matrix $$\left[\begin{array}{cccc} 1 & 4 & 0 & 6 \\ 4 & 2 & -1 & 0 \\ 0 & 1 & 5 & -6 \end{array}\right] \text { ? }$$Which of the following systems has augmented matrix \left\begin{array}{cccc}1 &amp; 4 &amp; 0 &amp; 6 \\ 4 &amp; 2 &amp; -1 &amp; 0 \\ 0 &amp; 1 &am ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The system $$\left\{\begin{array}{c} x+2 y-3 z=4 \\ 3 x-y+5 z=2 \\ 4 x+y+2 z=-2 \end{array}\right.$$ 0 answers 4 views The system $$\left\{\begin{array}{c} x+2 y-3 z=4 \\ 3 x-y+5 z=2 \\ 4 x+y+2 z=-2 \end{array}\right.$$The system $$\left\{\begin{array}{c} x+2 y-3 z=4 \\ 3 x-y+5 z=2 \\ 4 x+y+2 z=-2 \end{array}\right.$$ &nbsp; A. has a uni ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 $$\text { Write the system }\left\{\begin{array}{l} z=x+y \\ x-y=3 \text { in the form } A X=B \text {. Then } \\ x=-y \end{array}\right.$$ 0 answers 3 views $$\text { Write the system }\left\{\begin{array}{l} z=x+y \\ x-y=3 \text { in the form } A X=B \text {. Then } \\ x=-y \end{array}\right.$$ \text { Write the system }\left\{\begin{array}{l} z=x+y \\ x-y=3 \text { in the form } A X=B \text {. Then } \\ x=-y \end{array}\righ ... close 0 answers 8 views $$\text { The rank of the coefficient matrix } A=\left[\begin{array}{ccc} 1 & 2 & -3 \\ 3 & -1 & 5 \\ 4 & 1 & 2 \end{array}\right] \text { equals: }$$ \text { The rank of the coefficient matrix } A=\left\begin{array}{ccc} 1 &amp; 2 &amp; -3 \\ 3 &amp; -1 &amp; 5 \\ 4 &amp; 1 &amp; 2 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The augmented matrix of a system A X=B has been transformed using elementary row operations to ... 0 answers 3 views The augmented matrix of a system A X=B has been transformed using elementary row operations to ... \begin{aligned} &amp;\text { The augmented matrix of a system } A X=B \text { has been transformed using elementary row }\\ &amp ... close 0 answers 9 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the product of A, B and C? 0 answers 3 views What is the product of A, B and C? \text { Given } A=\left\begin{array}{ll} 4 &amp; 5 \end{array}\right, B=\left\begin{array}{llll} 1 &amp; 1 &amp; 2 &amp; 1 \end{ar ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let A be an n \times n matrix with I_{n} the identity matrix. The statement det A \neq 0 is equivalent to: 0 answers 5 views Let A be an n \times n matrix with I_{n} the identity matrix. The statement det A \neq 0 is equivalent to:Let A be an n \times n matrix with I_{n} the identity matrix. The statement det A \neq 0 is equivalent to: &nbsp; A. All the given options a ... close 0 answers 8 views $$\text { Let matrices } A \text { and } B \text { be given by } A=\left[\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & i \end{array}\right]$$ \begin{aligned} &amp;\text { Let matrices } A \text { and } B \text { be given by } A=\left\begin{array}{lll} a &amp; b &amp; c \\ d ... close 0 answers 6 views close 0 answers 5 views $$\text { Let } A=\left[\begin{array}{ccc} 3 & 2 & -1 \\ 1 & 6 & 3 \\ 2 & -4 & 0 \end{array}\right]$$ Then the diagonal entries of the adjoint of A are: \text { Let } A=\left\begin{array}{ccc} 3 &amp; 2 &amp; -1 \\ 1 &amp; 6 &amp; 3 \\ 2 &amp; -4 &amp; 0 \end{array}\right \end{equati ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The system of linear equations \begin{gathered} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{gathered} $$0 answers 2 views The system of linear equations$$ \begin{gathered} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{gathered} $$The system of linear equations$$ \begin{gathered} x-2 y+z=1 \\ -2 x+4 y-2 z=-3 \\ -x+2 y-z=-2 \end{gathered} $$has &nbsp; A) infinitely many solut ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let A and B be two square invertible matrices of the same order. Then \left((A B)^{T}\right)^{-1} is equal to 0 answers 3 views Let A and B be two square invertible matrices of the same order. Then \left((A B)^{T}\right)^{-1} is equal toLet A and B be two square invertible matrices of the same order. Then \left((A B)^{T}\right)^{-1} is equal to &nbsp; A) \left(B^{T}\right)^{- ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \vec{a}=(2,1,-1) and \vec{b}=(-1,2,1), then 2 \vec{a}-3 \vec{b} is equal to 0 answers 9 views If \vec{a}=(2,1,-1) and \vec{b}=(-1,2,1), then 2 \vec{a}-3 \vec{b} is equal toIf \vec{a}=(2,1,-1) and \vec{b}=(-1,2,1), then 2 \vec{a}-3 \vec{b} is equal to &nbsp; A) (1,-4,-5) B) (7,-4,5) C) (7,-4,-5) D) (7,4, ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the equation$$ z^{3}+8 i=0 $$0 answers 5 views Solve the equation$$ z^{3}+8 i=0 $$Solve the equation$$ z^{3}+8 i=0 $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve the system$$ \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}\$ ...