Project Using the Transformation A=[[1],[5],[6]] , x=[[1,-2,8]]

Problem

A=[[1],[5],[6]],x=[[1,−2,8]]

Solution

1. Identify the dimensions of the given matrices. Matrix A is a 3×1 column vector and matrix x is a 1×3 row vector.

2. Determine the operation for the projection transformation. In linear algebra, the projection matrix or the outer product of a vector A and a vector x is found by multiplying the column vector by the row vector.

3. Set up the matrix multiplication A*x This will result in a 3×3 matrix where each element (i,j) is the product of (A_i) and (x_j)

4. Calculate the first row by multiplying (A_1)=1 by each element of x 1(1) = 1,(-2) = -2,a*n*d(8) = 8$.

5. Calculate the second row by multiplying (A_2)=5 by each element of x 5(1) = 5,(-2) = -10,a*n*d(8) = 40$.

6. Calculate the third row by multiplying (A_3)=6 by each element of x 6(1) = 6,(-2) = -12,a*n*d(8) = 48$.

Final Answer

[[1],[5],[6]]*[[1,−2,8]]=[[1,−2,8],[5,−10,40],[6,−12,48]]

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