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Math 10B Spring 2018 Matrix Algebra Worksheet 1 Solutions (i)Write 2 2 matrices A, B, C such that AB = AC but B 6= C. Solution: First, a helpful observation. Suppose A is invertible and AB = AC. Then multiplying both sides by A 1 gives A 1(AB) = A 1(AC). Using distributivity and the fact that A 1A = I, this implies that IB = IC and therefore B = C.
Solutions and Hints for Selected Exercises Matrix Algebra by James E. Gentle. Exercises Beginning on Page 63. 2.1a. Assume {v1, v2, . . ., vk} is a linearly independent set of vectors. Now consider the pair of vectors vi and vk. If {vi, vj} is not linearly indepen-dent, then there exist ai and aj, not both 0, such that aivi + ajvj = 0.
Obviously the solution is. x = 1 2(b1 + b2); y = 1 2(b1 b2) Using Matrix Notation, I. Matrix notation allows the two equations. 1x + 1y = b1 1x 1y = b2. to be expressed as. 1. y x = b1 b2. or as Az = b, where. = A 1 1. 1. ; z = y x ; and. = b b1 : b2. Here A; z; b are respectively: (i) the coe cient matrix;
The 2 2× matrix A, is defined as 2 2 a b = − A where a and b are constants. The matrix A, maps the point P(2,5) onto the point Q( 1,2)− . a) Find the value of a and the value of b. A triangle T1 with an area of 9 square units is transformed by A into the triangle T2. b) Find the area of T2. a = − 1 , b = 6 , area 18=
These pages are a collection of facts (identities, approxima-tions, inequalities, relations, ...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference .
Lecture Notes 1: Matrix Algebra Part B: Determinants and Inverses. Peter J. Hammond. revised 2020 September 14th. Outline. Special Matrices. Square, Symmetric, and Diagonal Matrices. The Identity Matrix The Inverse Matrix Partitioned Matrices. Permutations and Their Signs.
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