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Properties of Matrices (Edexcel A Level Further Maths: Core Pure): Exam Questions

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1a
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bold italic M equals open parentheses table row 2 a 4 row 1 cell negative 1 end cell cell negative 1 end cell row cell negative 1 end cell 2 cell negative 1 end cell end table close parentheses

where a is a constant.

(a) For which values of a does the matrix M have an inverse?

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1b
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Given that M is non-singular,

(b) find M to the power of negative 1 end exponent in terms of a

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2
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bold italic M equals open parentheses table row k 5 7 row 1 1 1 row 2 1 cell negative 1 end cell end table close parentheses

Given that k not equal to 4, find, in terms of k, the inverse of the matrix bold M.

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3
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bold italic M equals open parentheses table row 2 cell negative 1 end cell 1 row 3 k 4 row 3 2 cell negative 1 end cell end table close parentheses where k is a constant

Find the values of k for which the matrix bold italic M has an inverse.

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