Math 224-01: Differential Equations: Reading Homework 7.2

1. Overview of Vectors and Matrices :
   
   1. Matrices and Operations : what is a matrix? a column vector?
      
      1. Point : how are matrices added? find

         (	1	2	) +	(	5	6	)
         	3	4			7	8

      2. Point : how is scalar multiplication with matrices done? find

         5 (	1	2	)
         	3	4

      3. Point : how is matrix multiplication done? find

         (	1	2	)	(	5	6	)
         	3	4			7	8

         
         
      4. Point : what is the 3 by 3 identity matrix?
         
      5. Point : what is the transpose of a matrix? what is the transpose of

         (	1	2	)
         	3	4

   2. Vector and Vector Spaces : what is a vector?
      
      1. Point : what is a linear combination of the vectors v¹ and v²?
         
      2. Point : what is the span of the vectors v¹ and v²?
         
   3. Matrices and Systems : write the differential equation y'' + 3y' + 2y = f(t) in matrix formulation.