# MTH 264

MTH 264 Written Homework 1 – S21 Due Monday April 12, 2021 First Name Last Name OSU Student ID # Instructions: Do all of your work on these papers. Scan the completed problems and create one PDF of your work. Your PDF needs to be at least the same number of pages as the original document. (If any of your work for a problem continues onto another page, please make a note of it on the first page of the problem and attach any additional pages to the end of your assignment.) Upload the PDF to this assignment in GRADESCOPE by the due date. (The Gradescope assignment can be accessed through Canvas.) (1) Consider the matrix   1 3 k A =  2 5 0 −2 1 3 (a) (1 point) For which value(s) of k is the determinant |A| equal to 0? (b) (1 point) For which value(s) of k does the system A~x = ~0 have a unique solution? Page 1 of 4 MTH 264 Written Homework 1 – S21 Due Monday April 12, 2021 (2) (4 points) Find the solution(s), if any, to the following system of equations by using row operations on an augmented matrix. Show your steps for credit!   =3 x + 2y −x + 3y + 3z = 0   y+z =1 Page 2 of 4 MTH 264 Written Homework 1 – S21 Due Monday April 12, 2021 (3) (2 points) Show that if A and B are invertible matrices of the same size, then (AB)−1 = B −1 A−1 . There is no need to consider specific matrices! Verify that the definition of inverse matrix is satisfied. (4) (2 points) Suppose A is a 4 × 5 matrix. What are the possible size(s) for a matrix C in each of the expressions A + C, AC, and CA? If the matrix (BA)2 is defined, what is the size of the matrix B? Page 3 of 4 MTH 264 Written Homework 1 – S21 Due Monday April 12, 2021 (5) (5 points) Find the inverse of the following matrix A using the algorithm [A|I] ∼ [I|A−1 ]. Show your steps for credit! (Hint: no fractions are required here. The inverse consists only of integers.)   1 0 2 A = 1 1 1 3 4 1 Page 4 of 4
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