Find a nonzeron×n matrix Awith identical entries such thatA2=A.
Consider two n x nmatrices A and B whose entries are positive or zero. Suppose that all entries of A are less than or equal to ‘s’, and all column sums of B are less than or equal to ‘r’ (the column sum of a matrix is the sum of all the entries in its column). Show that all entries of the matrix AB are less than or equal to ‘sr’.
Question 103: (This exercise builds on Exercise 49, 101, and 102.)
Question 107: Let ℕ be the set of all positive integers, 1, 2, 3,…. We define two functions f and g fromℕ to ℕ:
If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.
Decide whether the matrices in Exercises 1 through 15 are invertible. If they are, find the inverse. Do the computations with paper and pencil. Show all your work. 10.
Question: Refer to Exercise 10. Find the matrix of the reflection about the lineL.
Matrixis invertible for all real numbers k.
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