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4. For the following questions, choose true if the statement is always true, or false otherwise. A) ( True / False ) A homogeneous linear system of equations always has at least one solution. B) ( True / False ) A matrix in RREF form must contain only 1s and 0s. C) ( True / False ) Every matrix can be reduced to an RREF matrix. D) ( True / False ) If a linear system of equations is in echelon form, every variable is either leading or free, but not both. E) ( True / False ) A 2 !! 3 matrix may be multiplied by a 2 !! 3 matrix. F) ( True / False ) A 2 !! 3 matrix may be added to a 2 !! 3 matrix. G) ( True / False ) This set defines a line in ?3: { ? 0 1 2 ? + ? 1 1 1 ? z | z ? ? }. H) ( True / False ) If a linear system of equations has infinite solutions, one equation must be a multiple of another. I) ( True / False ) A linear system of equations that contains a 0 = 0 equation must have an infinite number of solutions. J) ( True / False ) An augmented matrix always has more rows than columns. 5. In your own words, explain how to create a set that represents a plane in 3-dimensional space. You may assume that you know specific points in the plane and vectors parallel to the plane, but you can't assume the plane has specific properties, like passing through the origin or being horizontal. A sketch may help.

          4. For the following questions, choose true if the statement is always true, or false otherwise.
A) ( True / False ) A homogeneous linear system of equations always has at least one solution.
B) ( True / False ) A matrix in RREF form must contain only 1s and 0s.
C) ( True / False ) Every matrix can be reduced to an RREF matrix.
D) ( True / False ) If a linear system of equations is in echelon form, every variable is either leading or free, but not both.
E) ( True / False ) A 2 !! 3 matrix may be multiplied by a 2 !! 3 matrix.
F) ( True / False ) A 2 !! 3 matrix may be added to a 2 !! 3 matrix.
G) ( True / False ) This set defines a line in ?3: { ? 0 1 2 ? + ? 1 1 1 ? z | z ? ? }.
H) ( True / False ) If a linear system of equations has infinite solutions, one equation must be a multiple of another.
I) ( True / False ) A linear system of equations that contains a 0 = 0 equation must have an infinite number of solutions.
J) ( True / False ) An augmented matrix always has more rows than columns.
5. In your own words, explain how to create a set that represents a plane in 3-dimensional space. You may assume that you know specific points in the plane and vectors parallel to the plane, but you can't assume the plane has specific properties, like passing through the origin or being horizontal. A sketch may help.

4. For the following questions, choose true if the statement is always true, or false otherwise.
A) ( True / False ) A homogeneous linear system of equations always has at least one solution.
B) ( True / False ) A matrix in RREF form must contain only 1s and 0s.
C) ( True / False ) Every matrix can be reduced to an RREF matrix.
D) ( True / False ) If a linear system of equations is in echelon form, every variable is either leading or free, but not both.
E) ( True / False ) A 2 !! 3 matrix may be multiplied by a 2 !! 3 matrix.
F) ( True / False ) A 2 !! 3 matrix may be added to a 2 !! 3 matrix.
G) ( True / False ) This set defines a line in ?3: ? 0 1 2 ? + ? 1 1 1 ? z | z ? ? .
H) ( True / False ) If a linear system of equations has infinite solutions, one equation must be a multiple of another.
I) ( True / False ) A linear system of equations that contains a 0 = 0 equation must have an infinite number of solutions.
J) ( True / False ) An augmented matrix always has more rows than columns.
5. In your own words, explain how to create a set that represents a plane in 3-dimensional space. You may assume that you know specific points in the plane and vectors parallel to the plane, but you can't assume the plane has specific properties, like passing through the origin or being horizontal. A sketch may help.

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