midterm-1

# midterm-1 - Math 54 Midterm 1 Review You can get a pdf of...

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Math 54 Midterm 1 Review You can get a pdf of this review sheet from my website: <http://math.berkeley.edu/ asmarks> The exam will cover material from the first 6 lectures: Lay chapters 1, 2, and 3 (excluding section 2.4 which wasn’t covered). You should expect the questions on the midterm to be very similar in difficulty and style to those on the homeworks. Some strategies for test taking For problems with equal point values, work on the easiest problems first. Don’t get stuck on a single question when there are others you could be doing much more quickly. Read all the questions carefully – you don’t want to lose points for misreading a question. Show all your work. This may increase the amount of partial credit you get, and helps you make fewer mistakes. Explain what you are doing if you use a theorem that is non-obvious. It’s worth taking an extra minute to write up your answers well. Check your work near the end of the exam to make sure that you’ve have answered each question entirely, especially multi-part questions. If you have time, check your work for logical and arithmetic mistakes. If you still have time, check your work in any way you can. Solve problems a different way, draw pictures, do special cases, etc. You shouldn’t leave the exam until the last possible moment. Linear Equations (sections 1.1-1.10) Understand systems of linear equations. Know all three row operations, and be able to use them to solve a system of linear equations. Be able to tell if a system has a unique solution, infinitely many solutions, or no solutions. Be able to form the augmented matrix and component matrix for a system of linear equations. Know the definitions of row echelon form, reduced row echelon form, and pivot positions. Be able to row reduce matrices to row echelon form and reduced row echelon form, and use this process to solve systems of linear equations. Be able to find the general solution of a system of linear equations. Watch out: you’ll lose points if you’re told to put a matrix in reduced row echelon form, and you only put the matrix in row echelon form. Know what vectors and scalars are. Know what a linear combination of vectors is. Know the definition of the span of a set of vectors. Know the correspondence between vectors equations, linear systems of equations, and matrix equa- tions: the vector equation x 1 a 1 + x 2 a 2 + . . . + x m a m = b where the x i are unknowns and the a i and b are constant vectors has the same solutions as the linear system whose augmented matrix is a 1 a 2 · · · a m b , which has the same solutions as the matrix equation A x = b where A is the matrix A = a 1 a 2 · · · a m . Be able to use this correspondence to solve vector and matrix equations.

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