Let a be a matrix which can be partitioned as follows 10 a3 where a, is an nxn matrix, a, is an mxm matrix, and 0 is a zero matrix (i. e., all its elements are zeros). (a) let a be an eigenvalue of a, with a corresponding eigenvector x. show that a is also an eigenvalues of a with a corresponding eigenvector (6) let b be an eigenvalue of a, with a corresponding eigenvector y. then in general b is also an eigenvalues of a with a corresponding eigenvector express the vector p in terms of a1, a2, a, b and y. (c) when does the statement in (b)not hold?

Customers are used to evaluate preliminary product designs. in the past, 93% of highly successful products received good reviews, 51% of moderately successful products received good reviews, and 14% of poor products received good reviews. in addition, 40% of products have been highly successful, 35% have been moderately successful and 25% have been poor products. round your answers to four decimal places (e.g. 98.) what is the probability that a product attains a good review? (b) if a new design attains a good review, what is the probability that it will be a highly successful product? (c) if a product does not attain a good review, what is the probability that it will be a highly successful product?