Write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2...

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Write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2 + 4x3 = 0 - 4x1-4x2 - 8x3 = 0 where the solution set is x = x2 X3 - 5x2 +10x3 = 0 x=x3 (Type an integer or simplified fraction for each matrix element.) Determine whether the statement below is true or false. Justify the answer. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below. A. The statement is false. The only solution of Ax = 0 is the zero vector. Thus, a nontrivial solution does not exist. B. The statement is false. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. C. The statement is true. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. D. The statement is true. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x cannot have any zero entries. A is a 25 matrix with two pivot positions. (a) Does the equation Ax = 0 have a nontrivial solution? (b) Does the equation Ax = b have at least one solution for every possible b? (a) Does the equation Ax = 0 have a nontrivial solution? No Yes (b) Does the equation Ax = b have at least one solution for every possible b? No Yes Determine if the vectors are linearly independent. Justify your answer. 5 7 8 0 -6 -27 The vector equation has so the vectors linearly independent. Write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2 + 4x3 = 0 - 4x1-4x2 - 8x3 = 0 where the solution set is x = x2 X3 - 5x2 +10x3 = 0 x=x3 (Type an integer or simplified fraction for each matrix element.) Determine whether the statement below is true or false. Justify the answer. If x is a nontrivial solution of Ax = 0, then every entry in x is nonzero. Choose the correct answer below. A. The statement is false. The only solution of Ax = 0 is the zero vector. Thus, a nontrivial solution does not exist. B. The statement is false. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. C. The statement is true. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x can have some zero entries so long as not all of its entries are zero. D. The statement is true. A nontrivial solution of Ax = 0 is a nonzero vector x that satisfies Ax = 0. Thus, a nontrivial solution x cannot have any zero entries. A is a 25 matrix with two pivot positions. (a) Does the equation Ax = 0 have a nontrivial solution? (b) Does the equation Ax = b have at least one solution for every possible b? (a) Does the equation Ax = 0 have a nontrivial solution? No Yes (b) Does the equation Ax = b have at least one solution for every possible b? No Yes Determine if the vectors are linearly independent. Justify your answer. 5 7 8 0 -6 -27 The vector equation has so the vectors linearly independent.