Let three matrices A- 2 1- 4 1 - B- 3 4- 2 3 - and C- 3 -4- -2 3 - then find tr A - tr ABC 2 tr A BC 2 4 - tr A BC 3 8 - where trA represents trace of matrix A-

The correct option is A 6 A=| 2 amp; 1 4 amp; 1 | , B=| 3 amp; 4 2 amp; 3 | , C=| 3 amp; 4 2 amp; 3 | ...

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Inverse of a Matrix

Let three mat...

Question

Let three matrices $A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}]$ ; $B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]$ and $C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]$ then find
$t r (A) + t r (\frac{A B C}{2}) t r (\frac{A {(B C)}^{2}}{4}) + t r (\frac{A {(B C)}^{3}}{8}) + . . . . + \infty$ , where $t r (A)$ represents trace of matrix $A$ .

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A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}] B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]

C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A ({B C)}^{2}}{4}) + t r (\frac{A ({B C)}^{3}}{8}) + . . . . . . . . . . . . . + \infty

t r (A)

A

[\begin{matrix} 2 & 1 4 & 1 \end{matrix}]; B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}] a n d C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

t_{r} (A) + t_{r} (\frac{A B C}{2}) + t_{r} (\frac{A (B C)^{2}}{4}) + t_{r} (\frac{A (B C)^{3}}{8}) + . . . . + \infty

A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}]

B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}]

C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}]

t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A {(B C)}^{2}}{4}) + t r (\frac{A {(B C)}^{3}}{8}) + . . . . . . . . + \infty =

A = [\begin{matrix} 2 & 1 4 & 1 \end{matrix}], B = [\begin{matrix} 3 & 4 2 & 3 \end{matrix}] and C = [\begin{matrix} 3 & - 4 - 2 & 3 \end{matrix}],

t r (A) + t r (\frac{A B C}{2}) + t r (\frac{A (B C)^{2}}{4}) + t r (\frac{A (B C)^{3}}{8}) + . . . \infty

A B C = I

tr (A B C + B C A + C A B)

A, B, C

3

tr (A)

A

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