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151.

Syntax error from line 1 column 1352 to line 1 column 1359.

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152.

Given space that space straight A equals space open square brackets table row cell negative 4 end cell cell space space space 4 end cell cell space space 4 end cell row cell negative 7 end cell cell space space 1 end cell cell space space space 3 end cell row 5 cell space space minus 3 end cell cell space space minus 1 end cell end table close square brackets space space and space space straight B space equals space open square brackets table row 1 cell space space minus 1 end cell cell space space 1 end cell row 1 cell space space minus 2 end cell cell space space minus 2 end cell row cell negative 2 end cell cell space space 1 end cell cell space space space space 3 end cell end table close square brackets space Find space AB. space Use space this space to space solve space the space following space system space of space linear space equations space colon space space straight x space – space straight y space plus space straight z space equals space 4 comma straight x space – space 2 straight y space – space 2 straight z space equals space 9 comma space 2 space straight x space plus space straight y space plus space 3 space straight z space equals space 1.

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153.

Given space that space straight A equals space open square brackets table row 1 cell negative 1 end cell cell space space 0 end cell row cell 2 space end cell cell space space space 3 end cell cell space space space 4 end cell row 0 cell space space 1 end cell cell space space 2 end cell end table close square brackets space and space straight B equals space open square brackets table row 2 cell space space space 2 end cell cell negative 4 end cell row cell negative 4 end cell cell space space 2 end cell cell space space minus 4 end cell row 2 cell negative 1 end cell 5 end table close square brackets space Find space AB space space Use space to space solve space the space following space system space of space equations space straight x space minus space straight y space equals space 3 comma space 2 straight x space plus space 3 straight y space plus space 4 straight z space equals space 17 comma space straight y space plus space 2 straight z space equals space straight l.

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154.

Syntax error from line 1 column 1298 to line 1 column 1305.

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155.

Syntax error from line 1 column 2075 to line 1 column 2082.

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156.

If space straight A equals space open square brackets table row cell cos space straight theta end cell cell space space space straight i space sin space straight theta end cell row cell straight i space sin space straight theta end cell cell space space cos space straight theta end cell end table close square brackets comma space then space prove space by space principle space of space mathematical space induction space that straight A to the power of straight n space equals open square brackets table row cell cos space straight theta end cell cell space space space straight i space sin space straight theta end cell row cell straight i space sin space straight theta end cell cell space space cos space straight theta end cell end table close square brackets space where space straight n space element of space straight N.

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157.

If space straight A subscript straight alpha space end subscript equals space open square brackets table row cell cosα space end cell cell space space sin space straight alpha space end cell row cell negative sin space straight alpha space end cell cell space space cos space straight alpha space end cell end table close square brackets comma space then space show space that straight A subscript straight alpha space end subscript. space straight A subscript straight beta space end subscript equals straight A subscript straight alpha space end subscript plus space straight A subscript straight beta space end subscript space and space left parenthesis straight A subscript straight alpha space end subscript right parenthesis to the power of straight n space space equals straight A subscript n space alpha end subscript space where space straight n space element of space straight N.

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158.

. space If space straight A comma space straight B space are space square space matrices space of space the space same space order space such space that space AB space equals space BA comma space then space prove space by space induction space that space AB to the power of straight n equals space straight B space to the power of straight n space straight A. space Further comma space prove space that space left parenthesis AB to the power of right parenthesis straight n end exponent space equals space A to the power of n space B to the power of n space for space all space straight n space element of space straight N.

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159.

Syntax error from line 1 column 1632 to line 1 column 1639.

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Syntax error from line 1 column 16602 to line 1 column 16609.

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