I. (4 points) Let A be an m × n matrix and let B be an n × p matrix. If the seco
ID: 3169928 • Letter: I
Question
I. (4 points) Let A be an m × n matrix and let B be an n × p matrix. If the second row of A 2. (4 points) Let A be an m × n matrix and let B be an n × p matrix. Show that if the columns 3. (4 points) If u and v are vectors in R", what is the relationship between uv and vu? Are 4. (4 points) Let A be an nxn matrix. If A is invertible, show that A+A is invertible by finding consists only of zeros, what can be said about the second row of AB? Justify your answer of B are linearly dependent, then the columns of AB are also linearly dependent. they equal? Justify your answer a matrix C so that C(A + A) = (A + A)C = I. Note: you may guess what C is and then show that it satisfies the invertibility condition, but please write doum: we guess that 5. (4 points) You are running a computer code with given matrices A, B, and C that are all size n x n and invertible. You put the code into a subroutine to calculate the inverse of ABC but the subroutine gives an error indicating the matrix you gave it Show that the subroutine (written by someone else, not you) must be incorrect by showing that ABC is invertible by finding a matrix D so that (ABC)D-1 and D(ABC) = 1 does not have an inverse 6. (6 points) Suppose we have three matrices, A, B, and C all of size 2 x 2 and none of them are the zero matrix. One of your classmates write (as part of another problem) A second classmate of yours, looks at this, and says this cannot be true, for consider the matrices given in problem 10 of Section 2.1: -4 6 Classmate 2 says that AB-AC, but BC (a) (2 points) Check that classmate 2 is correct: does AB-AC? (b) (4 points) You suspect that classmate 1 is also correct under some condition. Under what condition on the matrix A is classmate 1 correct? Show that the matrix classmate 2 used for A does not satisfy that condition.Explanation / Answer
1. Ans)
In matrix multiplication row elements of the first matrix(A) is multiplied with column elements of the second matrix(B). If all elements of the row are zero in matrix A then the reultant matrix AB will have zeros in that row. So from given information A second row have all zeros , So matrix AB second row will be all zeros.