Mark each statement as true or False. Justify your answer. If true, cite a theorem or fact from class. If false, explain why by giving the correct answer or a counter example. (a) Every line of the form y = mx + b is a subspace of R². (b) A is a 4 x 4 matrix, and its reduced matrix is the identity matrix, then its determinant is 4. (c) Every linearly independent set of vectors in a vector space V, can be extended to a basis for V. (d) If T : R³ → R² is a linear transformation, a basis of the null space can have at most two vectors. (e) Column space(A) = Column space(B), where B is the reduced form of A.

Determine whether the statement below is true or false. Justify the answer. Every matrix equation Ax=b corresponds to a vector equation with the same solution set. Choose the correct answer below. A. This statement is false. The matrix equation Ax=b does not correspond to a vector equation with the same solution set. B. This statement is false. The matrix equation Ax=b only corresponds to an inconsistent system of vector equations. C. This statement is true. The matrix equation Ax=b is simply another notation for the vector equation X₁₁ +₂³₂ +---+X³ =b₁ where a,,..., a, are the columns of A. D. This statement is true. The matrix equation Ax=b is simply another notation for the vector equation X₁a₁ +X₂ª² + ……... +xa = b. where a₁... a are the rows of A. wrong

Use row operations to change the matrix to reduced form. [:::] 111 18 5 6 7 24 1 1 1 18 5 6 7 24

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