Matrices And Vectors : Matrix Products, Ax=B and Linear Combinations
Not what you're looking for?
Please see the attached file for the fully formatted problems.
Compute the products using the row vector rule for computing Ax. If a product is undefined, explain why.
1) 2) 3)
4) let A = and b = . Show that the equation Ax=b does not have a solution for all possible b, and describe the set of all b for which Ax=b does have a solution.
5) How many rows of A contain a pivot position? Does the equation Ax=b have a solution for each b in R?
Make appropriate calculations and justify your answers and mention an appropriate theorem.
A= b =
6) Do the columns of B span R? Does the equation Bx=y have a solution for each y in .
7) Let Does { } span ? Why or why not?
8) Let Does { } span ? Why or why not?
9) True or False
a) the equation Ax=b is referred to as a vector equation.
b) A vector b is a linear combination of t he columns of a matrix A if and only if the equation Ax=b has at least one solution.
c) The equation Ax=b is consistent if the augmented matrix {A b} has a pivot position in every row.
d) The first entry in the product Ax is a sum of products.
e) If the columns of an mxn matrix A span , then the equation Ax=b is consistent for each b in .
f) If A is a m x n matrix and if the equation Ax=b is inconsistent for some b in , then A cannot have a pivot in every row.
10) Let .
It can be shown that 3u-5v-w=0. Use the fact (and no row operations) to find that satisfy the equation
11) Construct a 3x3 matrix, not in echelon form, whose columns span . Show that the
matrix you construct has the desired property.
12) Could a set of 3 vectors in span all of ? Explain. What about n vectors in when m is less than n?
Purchase this Solution
Solution Summary
Matrix products, Ax=B and linear combinations are investigated and discussed. The solution is detailed and well presented.
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability