Homework SourseTrue or False 1 Given a square matrix if you add 3 times row
True or False:
1) Given a square matrix, if you add 3 times row 2 to row 1, the determinant is multiplied by 3.
2) For any mxn matrix A, if Col A = Rm, this implies m >= n.
3) For any mxn matrix A, and right hand side b in Rm, the solution set of the linear system Ax = b is a subspace of Rn.
4) The set of all functions on [0,1] with f(1/2) = 0 is a subspace of the vector space of all functions on [0,1].
5) det(A+B) = detA + detB
6) If you double every entry of a 3x3 matrix, its determinant is multiplied by 8.
Solution
1) Given a square matrix, if you add 3 times row 2 to row 1, the determinant is multiplied by 3. (FALSE)
2) For any mxn matrix A, if Col A = Rm, this implies m >= n. (FALSE)
3) For any mxn matrix A, and right hand side b in Rm, the solution set of the linear system Ax = b is a subspace of Rn. (TRUE)
4) The set of all functions on [0,1] with f(1/2) = 0 is a subspace of the vector space of all functions on [0,1]. (TRUE)
5) det(A+B) = detA + detB (TRUE)
6) If you double every entry of a 3x3 matrix, its determinant is multiplied by 8. (TRUE)
