Question: 1. Consider the matrix B = 0 8]- a) Write a basis for the row space. b) Write a basis for the column space. c)

1. Consider the matrix B = 0 8]- a) Write a basis for the row space. b) Write a basis for the column space. c) Write a basis for the nullspace. d) What is B2 ? 2. Determine whether each of the following is a basis for R3 . b )3. Consider the matrix m = 4 DOW 7 a) Are the rows of m linearly independent? Justify your conclusion. b) Are the columns of m linearly independent? Justify your conclusion. c) Find the nullspace of m, state it's dimension. d) Find the nullspace of m', state it's dimension.4. For any m x n matrix A, let C(A) denote the column space and N(A) denote the nullspace. a) The column space of A, C(A), is a subspace of what vector space? b) The row space of A, C(A ), is a subspace of what vector space? c) The nullspace of A, N(A), is a subspace of what vector space? d) The nullspace of AT, N(A?), is a subspace of what vector space? e) If the dimension of C(A) and C(A ) is equal to r, what is the dimension of N(A) and N(A ) ? 5. Consider the matrix A = + ONO+ a) Find a basis for the column space and state it's dimension. b) Find a basis for the nullspace and state it's dimension. c) Find a basis for the row space and state it's dimension. d) Find a basis for the nullspace of A and state it's dimension

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