1. Construct the matrix that scales by (S, S2, S3) relative to the point (C, C2,C3)....

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1. Construct the matrix that scales by (S₁, S2, S3) relative to the point (C₁, C2,C3). 2. Construct the matrix that magnifies the triangle (A,B,C) by the factor 3 while keeping vertex A fixed. A = (2,-1,8) B = (5,-3,9) and C = (0,-1,14) 3. Let R(A) denote the matrix that rotates (about the Z-axis) by angle A. Find an expression for R(A+B) and show that rotations commute; i.e., R(A)R(B) = R(B)R(A) = R(A+B) 4. Let A and B denote order-4 matrices, and let P be a point in homogeneous coordinates (a 4x1 matrix with the last component equal to 1). Specify the number of multiplies required to compute a) (AB) P b) A (BP) Note that no multiplies are required to compute the last row of (A B) or the last component of (BP). Explain why it is usually advantageous to combine transformations before applying them (despite the fact that case (a) requires more multiplications. 5. Show that translations and scalings commute among themselves, but not with each other; i.e., TT' = T' T and S S' = S' S, but TS and S T are generally not equal. 1. Construct the matrix that scales by (S₁, S2, S3) relative to the point (C₁, C2,C3). 2. Construct the matrix that magnifies the triangle (A,B,C) by the factor 3 while keeping vertex A fixed. A = (2,-1,8) B = (5,-3,9) and C = (0,-1,14) 3. Let R(A) denote the matrix that rotates (about the Z-axis) by angle A. Find an expression for R(A+B) and show that rotations commute; i.e., R(A)R(B) = R(B)R(A) = R(A+B) 4. Let A and B denote order-4 matrices, and let P be a point in homogeneous coordinates (a 4x1 matrix with the last component equal to 1). Specify the number of multiplies required to compute a) (AB) P b) A (BP) Note that no multiplies are required to compute the last row of (A B) or the last component of (BP). Explain why it is usually advantageous to combine transformations before applying them (despite the fact that case (a) requires more multiplications. 5. Show that translations and scalings commute among themselves, but not with each other; i.e., TT' = T' T and S S' = S' S, but TS and S T are generally not equal.

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Answer Here are the answers to all the questions very clearly 1Construct the matrix that scales by S1 S2 S3 relative to the point C1 C2 C3 To construct the scaling matrix for scaling by factors S1 S2 ... View the full answer