Question

The set GL2 ( R) is the collection of all 2 by 2 matrices with real entries whose determinant is ___________, answer with justification a) zero b) non zero c) unit d) 1​

Answer 1

b.non zero

i hope it is useful to you.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The set GL2 ( R) is the collection of all 2 by 2 matrices with real entries whose determinant is ____

a) zero

b) non zero

c) unit

d) 1

EVALUATION

We know that M₂(R) is the set of all 2 × 2 matrices whose elements are real numbers

Now GL2(R) is the set of all 2 × 2 non singular matrices whose elements are real numbers

Thus it can written as :

$\displaystyle\sf{GL2(R) = \bigg \{ \: \displaystyle\begin{pmatrix} a & b \\ c & d \end{pmatrix} \: : \sf{a,b,c,d \in \:R \: \: and \: \: ad - bc \ne 0} \bigg \} }$

Moreover GL2(R) form a group under matrix multiplication

FINAL ANSWER

Hence the correct option is b) non zero

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