Tag: algebra

Let $A+2B=\begin{bmatrix} 1 & 2 & 0 \ 6 & -3 & 3 \ -5 & 3 & 1 \end{bmatrix}$ and $2A-B=\begin{bmatrix} 2 & -1 & 5 \ 2 & -1 & 6 \ 0 & 1 & 2 \end{bmatrix}$, then $tr(A)-tr(B)$ has the value equal to

If $A = \begin{bmatrix}2 & 3 & 4\ 5 & -3 & 8\ 9 & 2 & 16\end{bmatrix}$, then trace of A is,

If $A=[a _{ij}] _{n\times n}$ and $a _{ij}=i(i+j)$ then trace of $A=$

Let $A$ be the $2\times2$ matrices given by $A=\left[a _{ij}\right]$ where $a _{ij} = \left{0,1,2,3,4\right}$ such that $a _{11} + a _{12} + a _{21} + a _{22} = 4$
Find the number of matrices $A$ such that the trace of $A$ is equal to 4

If $A=[a _{ij}]$ is a scalar matrix then the trace of $A$ is

If $A=\begin{bmatrix} 2 & 1 \ 4 & 1 \end{bmatrix}; B=\begin{bmatrix} 3 & 4 \ 2 & 3 \end{bmatrix}$ and $C=\begin{bmatrix} 3 & -4 \ -2 & 3 \end{bmatrix}$ then $tr(A)+tr\left( \dfrac { ABC }{ 2 }  \right) +tr\left( \dfrac { A{ \left( BC \right)  }^{ 2 } }{ 4 }  \right) +tr\left( \dfrac { A{ \left( BC \right)  }^{ 3 } }{ 8 }  \right) +......\infty $ =

Consider three matrices A= $ \begin{bmatrix} 2 & 1 \ 4 & 1 \end{bmatrix} $, $ B = \begin{bmatrix} 3 & 4 \ 2 & 3 \end{bmatrix} $ and $ C = \begin{bmatrix} 3 & -4 \ -2 & 3 \end{bmatrix} $ Then the value of the sum 
$ tr(A)+tr \cfrac {(ABC) } {2} +tr \cfrac {A( {BC})^2} {4}+ \cfrac {A( {BC})^3} {2}  +...+ \infty               $is

 $P=\left[ \begin{matrix} { 5a }^{ 2 }+2bc & 6 & 8 \ 13 & { 8b }^{ 2 }-10ac & -9 \ -7 & 5 & { 25c }^{ 2 } \end{matrix} \right]$ and $Q=\left[ \begin{matrix} { a }^{ 2 }+6bc & 3 & 5 \ 12 & { -b }^{ 2 } & 6 \ 1 & 4 & { 17bc }^{ 2 } \end{matrix} \right] a,b$ & $c \epsilon N$, if trace $\left(P\right)=trac\left(Q\right)$, and $a,b$ & $C$ are sides of $\Delta ABC$ with $BC=a,CA=b$ & $AB=C$ then $\cos A$ is:

If $\left( \begin{array} { l l } { 3 } & { 2 } \ { 7 } & { 5 } \end{array} \right) A \left( \begin{array} { c c } { - 1 } & { 1 } \ { - 2 } & { 1 } \end{array} \right) = \left( \begin{array} { c c } { 2 } & { - 1 } \ { 0 } & { 4 } \end{array} \right)$  then trace of  $A$  is equal to

Let  $A=\left[ \begin{matrix} p & q \ q & p \end{matrix} \right] $ such that det(A)=r where p,q,r all prime numbers, then trace of A is equal to