Math Help - Matrix questions

1. Matrix questions

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I need help with (5) and (24). For (5), i can find MU and MV but have difficulty in finding M^nU and M^nV. For (24), i can solve (i) but don't know how to find (A+I)^21B.

The answer for (5): M^nU=6^nu; M^nV=9^nV...

As for (24) (A+I)^21B =
row1: (-3 1 5)
row2: (6 -2 -10)
row3: (3 -1 -5)

2. Originally Posted by MichaelLight
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I need help with (5) and (24). For (5), i can find MU and MV but have difficulty in finding M^nU and M^nV. For (24), i can solve (i) but don't know how to find (A+I)^21B.

The answer for (5): M^nU=6^nu; M^nV=9^nV...

Induction: $MU=\binom{6}{6}\,,\,\,M^2U=\binom{36}{36}\,\ldots\ ,M^nU\M(M^{n-1}U)=M\binom{6^{n-1}}{6^{n-1}}=\binom{6\cdot 6^{n-1}}{6\cdot 6^{n-1}}=\binom{6^n}{6^n}$

Try now to find and eventually prove a similar expression with V.

Tonio

As for (24) (A+I)^21B =
row1: (-3 1 5)
row2: (6 -2 -10)
row3: (3 -1 -5)