matrix. linear algebra

1.) Give an example of a 1 x 2 matrix. ie your entries are real numbers and please use | ] brackets to indicate a matrix. 2.) A = (ajj)2x3 =23 What is the value of aza? 3.) Let A be the matrix in previous question. If we can add matrix B to A; what is the size of B 4.) True or False : 32 = Z + Z + Z when Z is a matrix. 5.) Let X = 3 1 :6=B Find each of the following. If the operation cannot be done : state undefined operation. a) XE b) EX c) XX where X stands for the transpose of X 6.) Let 0 be the zero matrix. Write out the matrix if of size 2 x 2 7.) If we have a linear equation; what is the power of the variable(s) involved? 8.) Consider the linear equation 20 + 36 = 4 Is (a;b) = (1; ) a solution to the equation? Motivate your answer. 9.) Look up what is meant by a system of linear equations. A known fact of solutions of systems of linear equations is that only one the following options can hold : (i) No solution possible (ii) A unique solution can be found (iii) The system has infinite solutions. Consider that two straight lines form a linear system. Interpret what happens geometrically to the straight lines to get each case of the solution types given above. 10.) Look up the concept of a homogeneous linear system. Which of the following linear systems is homogeneous. [just give the answer I) or II) or III) : no motivation is required.] Ar + 14y = 0 & 2x - 3y = 7 II) 7x + 2y = 10 & llx - 0y = 7 III) 4r - 23y = 0 7x - 3y = 0 11.) You have a linear homogeneous system in three variables. Give a solution that this system must have