1. Find two (distinct) 2 x 2 matrices A and B such that AB = BA....

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1. Find two (distinct) 2 x 2 matrices A and B such that AB = BA. (Neither A nor B can be 12 or the zero matrix.) You must show that AB = BA. 2. The length or norm of u € R" is the non-negative scalar ||u||, defined by ||u|| 3 √√√x² + x² + ··· + u2. Compute the length of u given that u = -5 4 = 3. If ||u|| = 1, then u is called a unit vector. Find a unit vector in R³. Explain/show why it is a unit vector. /u.u= 4. Read the notes and section 6.1 about distance. Once you have done that, write "done" for this problem. 3a 2b + 5d = 7 -b+c-d=0 ла + 2c + 3d = -2 5. Review the three theorems listed at the end of the "Matrix Operations and Classes" notes. In Theorem 3 (2), (A + B)¹ = AT + BT. In Theorem 3 (4), (AB)T = BT AT. (Fill those details in in your notes.) Write (for this assignment) a detailed justification as to why (AB)T = BT AT. 6. Consider the following system of equations. (a) Write this system of equations in vector form. (b) Write this system of equations as an augmented matrix. 1. Find two (distinct) 2 x 2 matrices A and B such that AB = BA. (Neither A nor B can be 12 or the zero matrix.) You must show that AB = BA. 2. The length or norm of u € R" is the non-negative scalar ||u||, defined by ||u|| 3 √√√x² + x² + ··· + u2. Compute the length of u given that u = -5 4 = 3. If ||u|| = 1, then u is called a unit vector. Find a unit vector in R³. Explain/show why it is a unit vector. /u.u= 4. Read the notes and section 6.1 about distance. Once you have done that, write "done" for this problem. 3a 2b + 5d = 7 -b+c-d=0 ла + 2c + 3d = -2 5. Review the three theorems listed at the end of the "Matrix Operations and Classes" notes. In Theorem 3 (2), (A + B)¹ = AT + BT. In Theorem 3 (4), (AB)T = BT AT. (Fill those details in in your notes.) Write (for this assignment) a detailed justification as to why (AB)T = BT AT. 6. Consider the following system of equations. (a) Write this system of equations in vector form. (b) Write this system of equations as an augmented matrix.

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1One possible example of two distinct 2x2 matrices A and B that satisfy AB BA is A 1 0 0 1 B 0 1 1 0 ... View the full answer