Fall 2007 Exam 2
... Note that even though A has a row of zeros, AT A does not have a row of zeros. Moreover, A is a 4 × 3 matrix, so det A is not defined. (b) (3 points) Your friend (who, sadly, is not enrolled in Linear Algebra) claims that there is no such thing as 4-space, and thus, there is no such thing as a 3-box ...
... Note that even though A has a row of zeros, AT A does not have a row of zeros. Moreover, A is a 4 × 3 matrix, so det A is not defined. (b) (3 points) Your friend (who, sadly, is not enrolled in Linear Algebra) claims that there is no such thing as 4-space, and thus, there is no such thing as a 3-box ...
Systems of Equations - Elimination with Multiplication.notebook
... Solving Systems of Equations by Elimination Use addition to "eliminate" one variable. 1. Write the equations in column form. 2. If the coefficients of the terms are additive inverses (10 and -10, 5 and -5), they can be added to eliminate that variable. 3. If the coefficients are not additive inverse ...
... Solving Systems of Equations by Elimination Use addition to "eliminate" one variable. 1. Write the equations in column form. 2. If the coefficients of the terms are additive inverses (10 and -10, 5 and -5), they can be added to eliminate that variable. 3. If the coefficients are not additive inverse ...
8.4 Column Space and Null Space of a Matrix
... combination of the columns of A. Give the vector equation that you are trying to solve, and your row reduced augmented matrix. Be sure to tell whether u1 is in the column space of A or not! Do this with a brief sentence. (b) If u1 IS in the column space of A, give a specific linear combination of th ...
... combination of the columns of A. Give the vector equation that you are trying to solve, and your row reduced augmented matrix. Be sure to tell whether u1 is in the column space of A or not! Do this with a brief sentence. (b) If u1 IS in the column space of A, give a specific linear combination of th ...
Chapter 6. Linear Equations
... chosen row by the same combination with the corresponding entry of the ‘other’ row.] (iii) Exchange the positions of some pair of rows in the matrix. We see that the first two types, when you think of them in terms of what is happening to the linear equations, are just the sort of steps we did with ...
... chosen row by the same combination with the corresponding entry of the ‘other’ row.] (iii) Exchange the positions of some pair of rows in the matrix. We see that the first two types, when you think of them in terms of what is happening to the linear equations, are just the sort of steps we did with ...
Similarity and Diagonalization Similar Matrices
... matrix D such that A is similar to D — that is, if there is an invertible matrix P such that P −1 AP = D. Note that the eigenvalues of D are its diagonal elements, and these are the same eigenvalues as for A. Theorem 4.23. Let A be an n × n matrix. Then A is diagonalizable if and only if A has n lin ...
... matrix D such that A is similar to D — that is, if there is an invertible matrix P such that P −1 AP = D. Note that the eigenvalues of D are its diagonal elements, and these are the same eigenvalues as for A. Theorem 4.23. Let A be an n × n matrix. Then A is diagonalizable if and only if A has n lin ...
17.4 Connectivity - University of Cambridge
... the set Sj+1 can be found by examining Sj . If the component containing v is not the whole graph, the procedure can be reapplied starting from some vertex w not so far reached, and so on until all components are found. Question 3 Implement these algorithms and compare them to each other and to the f ...
... the set Sj+1 can be found by examining Sj . If the component containing v is not the whole graph, the procedure can be reapplied starting from some vertex w not so far reached, and so on until all components are found. Question 3 Implement these algorithms and compare them to each other and to the f ...
