3. Suppose a matrix G that performs a 3-entry rolling sum of a vector x, i.e., GX = (X₁, X₁ + X2, X1 + X2 + X3, ..., Xn−2 + Xn−1 + Xn). (a) Find G. (b) Is the matrix G invertible? Justify without using a determinant. (c) Find a matrix H such that GH = I. Show that your expression for H satisfies GH = I.
3. Suppose a matrix G that performs a 3-entry rolling sum of a vector x, i.e., GX = (X₁, X₁ + X2, X1 + X2 + X3, ..., Xn−2 + Xn−1 + Xn). (a) Find G. (b) Is the matrix G invertible? Justify without using a determinant. (c) Find a matrix H such that GH = I. Show that your expression for H satisfies GH = I.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 15CR
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