Determine if the statements are true or false. Any four vectors in R^3 are linea
ID: 3110952 • Letter: D
Question
Determine if the statements are true or false. Any four vectors in R^3 are linearly dependent. Any four vectors in R^3 span R^3. The rank of a matrix is equal to the number of pivots in its RREF. {v_1, v_2, ., v_n} is a basis for span(v_1, v_2, ., v_n). If v is an eigenvector of a matrix A, then v is an eigenvector of A + cI for all scalars c. (Her the identity matrix of the same dimension as A.) An n times n matrix A is diagonalizable if and only if it has n distinct eigenvalues. Let W be a subspace of R^n. If p is the projection of b onto W, then b - p elementof W^1.Explanation / Answer
1. true
because only 3 vectors in R^3 may independent
hence four vectors are dependent
2. false
3.false
because the matrix rank does not agrree with the rref in pivot
4.true