If A- 1 2 3- 4 5 6- 7 1 0- - B- 1 0 0- 0 3 0- 0 4 5- - then TrAB is

Name: JEE- Grade 12- Mathematics- Matrices and Determinants- Session 03- W19
Uploaded: 2022-07-04T10:36:42+05:30
Description: AB=.[ 1 amp;2 amp;3; 4 amp;5 amp;6; 7 amp;1 amp;0; ]..[ 1 amp; 0 amp;0; 0 amp;3 amp;0; 0 amp; 4 amp;5; ]. =.[ ...

AB=.[ 1 amp;2 amp;3; 4 amp;5 amp;6; 7 amp;1 amp;0; ]..[ 1 amp; 0 amp;0; 0 amp;3 amp;0; 0 amp; 4 amp;5; ]. =.[ ...

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Byju's Answer

Standard XII

Mathematics

Scalar Multiplication of a Matrix

If A=.[ 1 2 3...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 3 & 0 0 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦,$ then $T r (A B)$ is

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Solution

$A B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 3 & 0 0 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 18 & 15 4 & 39 & 30 7 & 3 & 0 \end{matrix} ⎤ ⎥ ⎦ \Rightarrow T r (A B) = 1 + 39 + 0 = 40$

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Q. If

A =

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦

B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 3 & 0 0 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦

,Tr (BA) =......

Q. If

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {0, 3, 4, 7}

B = {1, 2, 8, 9}

then

(A U B)^{'}

Q. If

⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 1 & 0 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 3 & 0 0 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦

T r (B A)

=______

The order of matrix $A = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 2 & - 2 & 4 & 3 & 1 0 & 9 & - 3 & - 1 & 0 0 & 0 & 5 & 0 & 0 - 2 & 0 & 0 & - 7 & - 1 - 1 & 0 & 0 & - 5 & 1 - 1 & - 2 & 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$ is ___