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In

`R^(3)`

we consider the following vectors

`vec(v)_(1)=(1,2,3),vec(v)_(2)(1,1,-1),vec(v)_(3)=(2,1,-4),vec(v)_(4)=(2,2,2)`

a) Is

`(vec(v)_(1),vec(v)_(2))`

a basis of

`R^(3)`

? (no calculation needed). Justify the answer b) Is

`(vec(v_(1)),vec(v_(2)),vec(v_(3)),vec(v_(4)))_(a )`

basis of

`R^(3)`

? (no calculation needed). Justify the answer c) Let

`B`

be the family

`(vec(v)_(1),vec(v)_(2),vec(v)_(3))`

. Write

`M_(B)`

its canonical matrix and calculate the determinant of

`M_(B)`

. Justify that

`B`

is a basis of

`R^(3)`

. d) Calculate the imvere of

`M_(B)`

by the method of your choice. e) What are the coordinater of

`vec(v)_(uarr)`

in the basis

`B`

.