document.write( "Question 1166866: Suppose A is a 3 × 3 matrix and consider the set
\n" ); document.write( "{I3,A,A2,A3,...,A9}. Explain why this set must be linearly dependent. \n" ); document.write( "

Algebra.Com's Answer #791416 by ikleyn(52775) $\"\"$ $\"About$

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document.write( "The linear space of 3x3 matrices is 9-dimensional space over the base field.\r\n" );
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document.write( "The list in the problem represents 10 (ten) elements of this linear space.\r\n" );
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document.write( "If in any finite-dimensional (n-dimensional) space you have the set of elements (\"vectors\") with the number of elements\r\n" );
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document.write( "more than n, the dimension of the space, then this set of elements is linearly dependent over the base field \r\n" );
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document.write( "(which is a GENERAL fact from linear algebra).\r\n" );
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