Any four vectors in R4 are linearly dependent See IMG True o

Any four vectors in R4 are linearly dependent

See IMG. True or False questions.

Determine it the statements are true or false 1. Any four vectors in R are linearty dependent. ? 2 Any four vectors in R\' span R 3. The rank of a matrix is equal to the number of pivots in its RREF. VV, Va) is a basis for span(Vi,V2 V) ? 5 If v is an eigenvector of a matrix A, then v is an True 5 eigenvector of A t cl tor all scalars e (Here I denotes the ide 6. An n x n matrix A is diagonalizable if and only ir t has n distinct eigenvalues 7Let W be a subspace of Rn, if p is the projection of b onto W, then b-pewi W, then b-peW ? ?

Solution

1.Flase. ...Any set of vector more than dim R^3 =3 ,are linearly dependent.

2.Flase. ....Not necessarily span.

3.True.......

4.Flase.....If it is linearly independent then it is basis.

5.Flase-....The eigen values correponding distinct eigen value are linearly independent ,not unique.

6.Flase......not necessarily.