Consider the matrix A = egin{bmatrix} 1 & 3 & 1 & 4 & -1 \ 0 & -5 & 7 & 2 & 0 \ -1 & 0 & 2 & 3 & 1 \ 0 & 3 & 2 & 1 & 0 \ 0 & 1 & 0 & 1 & 0 end{bmatrix} a) A is invertible. b) A is in row-echelon form. c) dim(Null A)=1. d) rank A=3. e) There is a vector b ? ?? such that Ax = b is not consistent. f) det(A)=0. g) dim(Null A)+rank A=4. Which of the statements above are true for A? (Submit the corresponding number without parentheses.) (1) a, d, e. (2) c, e, f. (3) c, f, g. (4) a, b, c, e. (5) c, e, f, g. (6) b, c, d, g. (7) a, b, c, e, f. (8) b, c, d, f, g. (9) b, c, e, f, g.
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A is invertible: For a matrix to be invertible, its determinant must be non-zero. We are given that det(A) = 0, so this statement is false. Show moreā¦
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