Question

1. If A is invertible, then the set of vectors made of the columns of A is linearly independent. True O False -1 ---{160.16) - 2. The set 10' 2| 0| 2-31 is a basis of R4 co True False 3. The set } is a subspace of Rº. 10 10 True False | |1] o] 1 **{0-0-0). 4. The set { 1] [ 1 , 0 , Lo 1] 1 1 } is a basis of R3. ) True False

Answer 1

1 I 1. If o is invertible, then the made set of veetors. of the columns of O is linearry indipendent y True. AS A is invertible, then det ato, therefore rank = order of the matrin.. therefore, row rank and column rank are equal and linearly indipendent of the column or now neetors.. since basis of 1R9 generally contains tour vectors and Here the set .. 5 vectors. contains Any one Therefore, can of as be them, linear expressed combination of others. ③2. Falsey • The set {Lo The set is a rector is a veetor ? This is a nurs subspace. This subspace of IR3 of IR3 ,it forms a triviar subspace of 'R] via sub is basis basis @ set the The set (1), (!), of IR I the set is dimension 3, lineasty indipendent so it span 1R3. since and