Which of the following sets with standard matrix addition and scalar multiplicat

Question

Which of the following sets with standard matrix addition and scalar multiplications form vector spaces? Choose all that apply. All matrices of any size. All singular matrices of size 2x 2 All invertible matrices of size 2 x 2 OAll 2 x 2 matrices, M22 QUESTION 2 Which of the following are a vector subspace of R3 with standard operations? Choose all that apply. Any plane in R Any plane through the origin in R The set of all points satisfying the equation 2x+5y +z-0 Any line through the origin in R3 U Any line in R The origin QUESTION 3 Which of the following is a vector subspace of Mnn,the space of all n xn matrices. Choose all that apply. The set of all nx n matrices for which all elements above diagonals are zero. (These matrices are called lower triangular matrices.) The set of all symmetric n × n matrices. The set of all n × n matrices where only the diagonal elements are nonzero. O The set of all singular nx n matrices.

Explanation / Answer

Question 1

1 false, 2 false , 3 false, 4   false,

Question 2

1. false, 2.true, 3 true, 4. true, 5. false, 6 true,   

Question 3

1 true, 2 true, 3 false, 4 false,

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