Final answer:
Matrix multiplication between a 4x2 and an 8x4 matrix is not possible because the number of columns in the first matrix does not equal the number of rows in the second. Two vectors with different magnitudes can add up to zero if they are in opposite directions, and with three or more vectors, there are many arrangements that can lead to a zero vector.
Step-by-step explanation:
You have a 4x2 matrix (mat1) and an 8x4 matrix (mat2). In order to perform matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Mat1 has 2 columns and mat2 has 8 rows, so these matrices cannot be multiplied together because the necessary condition for matrix multiplication is not satisfied.
Moving on to the general vector question, if you take two steps of different sizes, it is possible to end up at your starting point. More generally, two vectors can add up to zero if they have the same magnitude but are in opposite directions.
However, with three or more vectors, there are many more possibilities for arranging vectors so that their sum is zero, regardless of their individual magnitudes.
Finally, regarding the square sizes, Marta has a square with a side length of 4 inches and a larger square with side lengths twice as long. The area of a square is calculated by squaring the side length, so the larger square's side length is 8 inches, and its area is 8 x 8, which is 64 square inches.
This means the larger square has an area that is four times greater than the smaller square, which has an area of 16 square inches (4 x 4).