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13 Find (where possible) the inverse of the matrices 21 -1 1457 132 B= 2 1 3 -12 -13 2, Are these matrices singular or non-singular? A=

13 Find (where possible) the inverse of the matrices 21 -1 1457 132 B= 2 1 3 -12 -13 2, Are these matrices singular or non-singular? A=

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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13 Find (where possible) the inverse of the matrices 1457 A = 1 3 2 B= 2 1 3 -12 32 Are these matrices singular or non-singular? 14 Find the determinant of the matrix [2 1 31 A = 10 a 314 in terms of a. Deduce that this matrix is non-singular provided a 1 and find A in this case, 15 Find the inverse of 22 1 1-5-1 -1 -6 Hence find the equilibrium prices of the three-commodity market model given in Practice Problem 13 of Section 1.3. 16 (Maple) Use the Maple instruction det (A to find the determinant of the 4x4 matrix a 21-1 2 341 0-15 1 24-3 For what value of a does this matrix fail to possess an inverse? [Do not forget to load the linear algebra package before you begin. You do this by typing with (1inalg! : 17 (Maple) (a) Find the determinant of the general 3 x 3 matrix, A Lg h Deduce that this matrix is singular whenever the second row is a multiple of the first row. (b) Find the inverse, A, of the general 3 x 3 matrix given in part (a) and verify that AA-¹ =1.
Transcribed Image Text:13 Find (where possible) the inverse of the matrices 1457 A = 1 3 2 B= 2 1 3 -12 32 Are these matrices singular or non-singular? 14 Find the determinant of the matrix [2 1 31 A = 10 a 314 in terms of a. Deduce that this matrix is non-singular provided a 1 and find A in this case, 15 Find the inverse of 22 1 1-5-1 -1 -6 Hence find the equilibrium prices of the three-commodity market model given in Practice Problem 13 of Section 1.3. 16 (Maple) Use the Maple instruction det (A to find the determinant of the 4x4 matrix a 21-1 2 341 0-15 1 24-3 For what value of a does this matrix fail to possess an inverse? [Do not forget to load the linear algebra package before you begin. You do this by typing with (1inalg! : 17 (Maple) (a) Find the determinant of the general 3 x 3 matrix, A Lg h Deduce that this matrix is singular whenever the second row is a multiple of the first row. (b) Find the inverse, A, of the general 3 x 3 matrix given in part (a) and verify that AA-¹ =1.
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