Any four vectors in R4 are linearly dependent See IMG. True or False questions.

Question

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 ? ?

Explanation / Answer

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.

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