Question

If matrix A and matrix AB are given, determine the first and second columns of B. Let the first column of B be denoted as C1 and the second column as C2.

Answer 1

To determine the columns of matrix B, one can solve a system of equations derived from the product of matrix A and AB.

This involves matching the elements of the product to the corresponding dot products of rows from A with columns of B.

Step-by-step explanation:

If matrix A and matrix AB are given, it is possible to determine the first (C1) and second columns (C2) of matrix B using matrix multiplication rules.

To find these columns, one can set up a system of equations based on the given products of A and AB and solve for the elements in C1 and C2. By doing this, the system directly yields the values of the unknowns in terms of the elements of A and AB.

Typically, matrix multiplication involves taking the dot product of rows from matrix A with corresponding columns in B, which allows us to extract the components of C1 and C2. This is often performed in accordance with the standard basis vectors î, ķ, and Â, making sure to align scalar components such as Cx, Cy, and Cz correctly.