11. (9pts) (a) Suppose that the matrix P = (AB)TCD exists and is 4 x 4. Assuming that A is 3 x 5, B has 5 rows, and D has 2 rows, find the size of A, B, C, D.

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15 Jun 2023

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1. Suppose that A is a 3 x 4 matrix B is a 4x6 matrix, C is a 4x3 matrix and D is a 3 x 6 matrix. Consider the following: (1)(C+AT), (2) DDTC, (3) DBT(C-24"), (4) (AB-D)B",(5) (A" +3C)D (6) ACTDT-2C. Which of the following is true? (a) All six of these are defined. (b) None of these six are defined. (c) (1), (2), (3), (4) and (5) are defined; (6) is not. (d) (1), (3) and (4) are defined; (2), (5) and (6) are not defined. (e) None of the above

2. Suppose that C is a mxn matrix D is a pxq matrix, F is a r X s. Assume that the matrix CDT +CFT is well defined. Which of the following is true? (A)m=n=s=q and p=r B) m =n=p=q=r=s. C) m=n=p=s and q=r. D) m = p=n=. E) None of the above.

8. Suppose that A is a n xm matrix B is a p xq matrix, C is a r x s. Assume that the matrix B2A + BCT is well defined. Which of the following is true? A) n = m =p=q=r=s. B) n = m = p = s and q = r. (C) p = q = n = s and m = r D) q = p = m = r = s. E) None of the above.

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11. (9pts) (a) Suppose that the matrix P = (AB)TCD exists and is 4 x 4. Assuming that A is 3 x 5, B has 5 rows, and D has 2 rows, find the size of A, B, C, D.

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