3 2) (1.3) Is the vector 4 a linear combination of the vectors [] H Is...

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3 2) (1.3) Is the vector 4 a linear combination of the vectors [] H Is the span of the three vectors R³? 3) (1.4) Solve the matrix equation Ax = b using an augmented matrix where -4 A = [2] [_]. Write the solution as a vector. 31 2] and b = 4) (1.5) Write the solution set of the homogeneous system of equations in parametric vector form, x₁ + x₂ + 2x3 = 0 x₁ + x₂ = 0 x₂ + x3 = 0 5) (1.7) Determine if the vectors 6) (1.8/1.9) Show that the mapping T(x₁, x2, x3) = (2x₁ + x3, -x₁ - 3x2 + x3) is a linear transformation. T maps from what space to what space? 1 0 1 2 7) (2.1) For A = -1 0 When thought of as a matrix, what is the image of the vector L 0 and B = 1 ª are linearly independent. 3 5 0 [¦¤ 2 1-2 0? 2 5 0 -7 3? 3 4 find 2A + 3B, A. B, BT. A. 3 2) (1.3) Is the vector 4 a linear combination of the vectors [] H Is the span of the three vectors R³? 3) (1.4) Solve the matrix equation Ax = b using an augmented matrix where -4 A = [2] [_]. Write the solution as a vector. 31 2] and b = 4) (1.5) Write the solution set of the homogeneous system of equations in parametric vector form, x₁ + x₂ + 2x3 = 0 x₁ + x₂ = 0 x₂ + x3 = 0 5) (1.7) Determine if the vectors 6) (1.8/1.9) Show that the mapping T(x₁, x2, x3) = (2x₁ + x3, -x₁ - 3x2 + x3) is a linear transformation. T maps from what space to what space? 1 0 1 2 7) (2.1) For A = -1 0 When thought of as a matrix, what is the image of the vector L 0 and B = 1 ª are linearly independent. 3 5 0 [¦¤ 2 1-2 0? 2 5 0 -7 3? 3 4 find 2A + 3B, A. B, BT. A.

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3 To determine if the vector 4 1 2 is a linear combination of the vectors 2 1 0 and 1 4 3 we can set ... View the full answer