Terms related to matrices - class-XII
Description: terms related to matrices | |
Number of Questions: 40 | |
Created by: Ankita Patil | |
Tags: maths matrices and determinants algebra matrices |
For what value of
k, the matrix $A = \begin{bmatrix} 4 & 3 -k\\ 1 & 2 \end{bmatrix}$ is
not invertible?
If the traces of $A, B$ are $20$ and $-8$, then the trace of $A+B$ is:
If $A$ is a $3\times3$ skew-symmetric matrix, then the trace of $A$ is equal to
If$A=\left[ \begin{matrix} 1 & -5 & 7 \ 0 & 7 & 9 \ 11 & 8 & 9 \end{matrix} \right] $ , then trace of matrix $A$ is
If $\displaystyle :A= \left [ a _{ij} \right ]$ is a scalar matrix of order $\displaystyle :n\times n$ such that $\displaystyle :a _{ij}= k $ for all then trace of A is equal to
If $\displaystyle :A= \left [ a _{ij} \right ]$ is a scalar matrix, then trace of A is
If A is a skew-symmetric matrix, then trace of A is
If $A=\begin{bmatrix} 1 & -5 & 7 \ 0 & 7 & 9 \ 11 & 8 & 9 \end{bmatrix}$, then the value of tr $A$ is
If $A = \left[ {{a _{ij}}} \right]$ and ${a _{ij}} = i\left( {i + j} \right)$ then trace of $A=$
If $tr(A)=3, tr(B)=5$, then $tr(AB)$=
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
Let 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 $t _r(A)+t _r\left(\dfrac{ABC}{2}\right)+t _r\left(\dfrac{A(BC)^2}{4}\right)+t _r\left(\dfrac{A(BC)^3}{8}\right)+.....+\infty =?$
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 $\displaystyle tr(A)+tr\left(\frac{ABC}{2} \right)+tr\left(\frac{A{(BC)}^{2}}{4} \right)+tr\left(\frac{A{(BC)}^{2}}{8} \right)+...+\infty= $
The trace of the matrix $A = \begin{bmatrix}1 & -5 & 7\ 0 & 7 & 9\ 11 & 8 & 9\end{bmatrix}$ is
If $A = [a _{ij}]$ is a scalar matrix of order $n\times n$ such that $a _{ii} = k$ for all $i$, then trace of $A$ is equal to
If $A$ is a $3\times 3$ skew-symmetric matrix, then trace of $A$ is equal to
If $A$ is $2\times 2$ matrix such that $A^2 = 0$, then $tr :(A)$ is
If $A =\begin{bmatrix} 1&9 & -7\ i & \omega^n & 8\ 1 & 6 &\omega^{2n} \end{bmatrix}$ where $i= \sqrt{-1} $ and $\omega$ is complex cube root of unity, then tr(A) will be
For $\alpha, \beta, \gamma \in R$, let $A=\begin{bmatrix} { \alpha }^{ 2 } & 6 & 8 \ 3 & { \beta }^{ 2 } & 9 \ 4 & 5 & { \gamma }^{ 2 } \end{bmatrix}$ and $B=\begin{bmatrix} 2\alpha & 3 & 5 \ 2 & 2\beta & 6 \ 1 & 4 & 2\gamma -3 \end{bmatrix}$. If ${ T } _{ r }(A)={ T } _{ r }(B)$ then the value of $\left( \cfrac { 1 }{ \alpha } +\cfrac { 1 }{ \beta } +\cfrac { 1 }{ \gamma } \right) $ is-
i. Trace of the matrix is called sum of the elements in a principle diagonal of the square matrix.
ii. The trace of the matrix $\begin{bmatrix}
8 & 7 &5\
5 &8 & 2\
7 & 2 & 8
\end{bmatrix}$ is 24 Which of the following statement is correct.
If $A=\begin{bmatrix}
1 &4 &7 \
2 &6 &5 \
3 &-1 &2
\end{bmatrix}$ and B $=$ diag (1 2 5), then
trace of matrix $AB^{2}$ is
Let 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 find
${ tr }\left( A \right) +{ 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 $, where $tr(A)$ represents trace of matrix $A$.
Elements of a matrix $A$ of order $10\times10$ are defined as ${ a } _{ ij }={ w }^{ i+j }$(where $w$ is cube root of unity), then trace ($A$) of the matrix is
Let $A=\left[\begin{matrix}2&0&7\0&1&0\1&-2&1\end{matrix}\right]$ and $B=\left[\begin{matrix}-x&14x&7x\0&1&0\x&-4x&-2x\end{matrix}\right]$ are two matrices such that $AB = (AB)^{-1}$ and $AB\ne I$ (where $I$ is an identity matrix of order $3\times3$).
Find the value of $Tr.\left(AB+(AB)^2+(AB)^3+...+(AB)^{100}\right)$ where $Tr.(A)$ denotes the trace of matrix $A$.
Let $A=\left[\begin{matrix}1 & \displaystyle\frac{3}{2}\1 & 2\end{matrix}\right], B = \left[\begin{matrix}4 & -3\-2 & 2\end{matrix}\right] \mbox{ and } C _r = \left[\begin{matrix}r.3^r & 2^r\0 & (r-1)3^r\end{matrix}\right]$ be 3 given matrices. Compute the value of $\sum _{r=1}^{50}{tr.\left((AB)^r C _r\right)}.($ where $tr.(A)$ denotes trace of matrix A $)$
Let $A=\left[\begin{matrix}3x^2\1\6x\end{matrix}\right], B=[a,b,c]$ and $C=\left[\begin{matrix}(x+2)^2&5x^2&2x\5x^2&2x&(x+2)^2\2x&(x+2)^2&5x^2\end{matrix}\right]$ be three given matrices, where $a,b,c$ and $x\in R$, Given that $tr.(AB) = tr.(C) \vee x\in R$, where $tr.(A)$ denotes trace of $A$. Find the value of $(a+b+c)$
If $f(x,y) = x^2 + y^2 - 2xy, \space (x,y \in R)$ and
$\quad A = \begin{bmatrix}f(x _1,y _1) & f(x _1,y _2) & f(x _1,y _3) \ f(x _2,y _1) & f(x _2,y _2) & f(x _2,y _3) \ f(x _3,y _1) & f(x _3,y _2) & f(x _3,y _3) \end{bmatrix}$
such that trace $(A) = 0$, then which of the following is true (only one option)
Let 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
$t _r(A)+t _r\left ( \frac{ABC}{2} \right )+t _r\left ( \frac{A(BC)^2}{4} \right )+t _r\left ( \frac{A(BC)^3}{8} \right )+....+\infty $