If A= $left[ {begin{array}{*{20}{l}} {frac{2}{3}}&1&{frac{5}{3}}

Hindi

3 and 4 .Determinants and Matrices

medium

If $A=$ $\left[ {\begin{array}{{20}{l}}
{\frac{2}{3}}&1&{\frac{5}{3}} \\
{\frac{1}{3}}&{\frac{2}{3}}&{\frac{4}{3}} \\
{\frac{7}{3}}&2&{\frac{2}{3}}
\end{array}} \right]$ and $B=$ $\left[ {\begin{array}{{20}{l}}
{\frac{2}{5}}&{\frac{3}{5}}&1 \\
{\frac{1}{5}}&{\frac{2}{5}}&{\frac{4}{5}} \\
{\frac{7}{5}}&{\frac{6}{5}}&{\frac{2}{5}}
\end{array}} \right],$ then compute $3A-5B.$

$\left[ {\begin{array}{*{20}{l}}
0&0&0 \\
0&0&0 \\
0&0&0
\end{array}} \right]$

Solution

$3A – 5B = $ $3\left[ {\begin{array}{*{20}{l}}
{\frac{2}{3}}&1&{\frac{5}{3}} \\
{\frac{1}{3}}&{\frac{2}{3}}&{\frac{4}{3}} \\
{\frac{7}{3}}&2&{\frac{2}{3}}
\end{array}} \right]$ $ – 5\left[ {\begin{array}{*{20}{l}}
{\frac{2}{5}}&{\frac{3}{5}}&1 \\
{\frac{1}{5}}&{\frac{2}{5}}&{\frac{4}{5}} \\
{\frac{7}{5}}&{\frac{6}{5}}&{\frac{2}{5}}
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
2&3&5 \\
1&2&4 \\
7&6&2
\end{array}} \right]$ $ – \left[ {\begin{array}{*{20}{l}}
2&3&5 \\
1&2&4 \\
7&6&2
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
0&0&0 \\
0&0&0 \\
0&0&0
\end{array}} \right]$

Standard 12

Mathematics

Assume $X,\, Y,\, Z,\, W$ and $P$ are matrices of order $2 \times n,\, 3 \times k,\, 2 \times p, \,n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7 X-5 Z$ is

medium

If $\omega \ne 1$ is cube root of unity and $H = \left[ {\begin{array}{*{20}{c}}\omega &0\\0&\omega \end{array}} \right]$ then ${H^{70}}$ is equal to

medium

(AIEEE-2011)

If $B = \left[ {\begin{array}{*{20}{c}}
5&{2\alpha }&1\\
0&2&1\\
\alpha &3&{ – 1}
\end{array}} \right]$ is the inverse of a $3 \times 3$ matrix $A$, then the sum of all values of $\alpha $ for which $det\, (A) + 1 = 0$, is

hard

(JEE MAIN-2019)

If $A = \left[ {\begin{array}{*{20}{c}}{\,\,\,\cos \alpha }&{\sin \alpha }\\{ – \sin \alpha }&{\cos \alpha }\end{array}} \right]$, then ${A^2} = $

easy

If a matrix has $18$ elements, what are the possible orders it can have? What, if it has $5$ elements ?

easy

Solution

Similar Questions

Assume $X,\, Y,\, Z,\, W$ and $P$ are matrices of order $2 \times n,\, 3 \times k,\, 2 \times p, \,n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7 X-5 Z$ is

If $\omega \ne 1$ is cube root of unity and $H = \left[ {\begin{array}{*{20}{c}}\omega &0\\0&\omega \end{array}} \right]$ then ${H^{70}}$ is equal to

If $B = \left[ {\begin{array}{*{20}{c}} 5&{2\alpha }&1\\ 0&2&1\\ \alpha &3&{ – 1} \end{array}} \right]$ is the inverse of a $3 \times 3$ matrix $A$, then the sum of all values of $\alpha $ for which $det\, (A) + 1 = 0$, is

If $A = \left[ {\begin{array}{*{20}{c}}{\,\,\,\cos \alpha }&{\sin \alpha }\\{ – \sin \alpha }&{\cos \alpha }\end{array}} \right]$, then ${A^2} = $

If a matrix has $18$ elements, what are the possible orders it can have? What, if it has $5$ elements ?

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If $B = \left[ {\begin{array}{*{20}{c}}
5&{2\alpha }&1\\
0&2&1\\
\alpha &3&{ – 1}
\end{array}} \right]$ is the inverse of a $3 \times 3$ matrix $A$, then the sum of all values of $\alpha $ for which $det\, (A) + 1 = 0$, is