Question

Let a = [1 1 1 2 3 5]. Construct a 2x3 matrix c (by trial and error) using only 1, 1, and 0 as entries, such that ca = ?. Compute ac and note that ac = ?.

Answer 1

To construct a 2x3 matrix 'c' using 1, 1, and 0 as entries, arrange the elements of vector 'a' in the matrix. Multiply matrix 'c' by vector 'a' to compute ca and multiply vector 'a' by matrix 'c' to compute ac.

Step-by-step explanation:

To construct a 2x3 matrix using 1, 1, and 0 as entries, such that ca = ?, we need to rearrange the elements of vector 'a' in a 2x3 matrix 'c' and multiply them. By trial and error, we can arrange the elements of 'a' as follows:

c = [1 1 1; 2 3 0]

To compute 'ca', we multiply the matrix 'c' by the vector 'a' using matrix multiplication.

ca = [1 1 1; 2 3 0] * [1; 1; 1; 2; 3; 5]

To compute 'ac', we multiply the vector 'a' by the matrix 'c' using matrix multiplication.

ac = [1; 1; 1; 2; 3; 5] * [1 1 1; 2 3 0]