Let w be the eigenvector of S corresponding to the second largest eigenvalue. In addition, let u beany arbitrary column vector, whose dimension is the same as that of w. Discuss whether the followingmatrix products are conformable (5 marks).• Yw• Yw′• ww′• u′w• S′Y

Sure, let's discuss the conformability of each of these matrix products:

1. Yw: This product is conformable if the number of columns in Y is equal to the number of rows in w. Since w is a column vector, it has only one column. Therefore, Y must have one column for the product to be conformable.

2. Yw′: This product is conformable if the number of columns in Y is equal to the number of rows in w′. Since w′ is a row vector, it has only one row. Therefore, Y must have one row for the product to be conformable.

3. ww′: This product is always conformable because the number of columns in w (which is 1, since w is a column vector) is equal to the number of rows in w′ (which is also 1, since w′ is a row vector).

4. u′w: This product is conformable if the number of columns in u′ (which is 1, since u′ is a row vector) is equal to the number of rows in w (which is also 1, since w is a column vector). Therefore, this product is always conformable.

5. S′Y: This product is conformable if the number of columns in S′ is equal to the number of rows in Y. Since S′ is the transpose of S, it has the same number of columns as S has rows. Therefore, the number of rows in Y must be equal to the number of rows in S for the product to be conformable.