Monthly Archives: July 2011

Linear Algebra and Its Applications, Review Exercise 1.12

Review exercise 1.12. State whether the following are true or false. If a statement is true explain why it is true. If a statement is false provide a counter-example. (a) If is invertible and has the same rows as but … Continue reading

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Linear Algebra and Its Applications, Review Exercise 1.11

Review exercise 1.11. Suppose is a 2 by 2 matrix that adds the first equation of a linear system to the second equation. What is ? ? ? Answer: Since adds the first equation to the second, we have We … Continue reading

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Linear Algebra and Its Applications, Review Exercise 1.10

Review exercise 1.10. Find the inverse of each of the following matrices, or show that the matrix is not invertible. Answer: We use Gauss-Jordan elimination on the first matrix , starting by multiplying the first row by 1 and subtracting … Continue reading

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Linear Algebra and Its Applications, Review Exercise 1.9

Review exercise 1.9. Show a 2 by 2 system of equations (i.e., two equations in two unknowns) that has an infinite number of solutions. Answer: One possibility is the following system: corresponding to the matrix equation where The solutions to … Continue reading

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Linear Algebra and Its Applications, Review Exercise 1.8

Review exercise 1.8. Given the following matrices: for a matrix how are the rows of related to the rows of ? Answer: For the first matrix , the product is a 3 by 3 matrix in which: The first row … Continue reading

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Linear Algebra and Its Applications, Review Exercise 1.7

Review exercise 1.7. For each of the each of the 2 by 2 matrices containing only -1 or 1 as entries, determine whether the matrix is invertible or not. Answer: A 2 by 2 matrix has four entries. If each … Continue reading

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Linear Algebra and Its Applications, Review Exercise 1.6

Review exercise 1.6. (a) For each of the each of the 2 by 2 matrices containing only 0 or 1 as entries, determine whether the matrix is invertible or not. (b) Of the 10 by 10 matrices containing only 0 … Continue reading

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