True or False 1. If p locates a point on a line l in R and if n + 0 is normal to l, then any other point x on l must satisfy n • x = n • p. 2. A binary vector is a vector with two components which are integers modulo 2. 3. If A is invertible, then the only solution to Ax = b is A-'b. 4. If a row of a matrix A is multiplied by a scalar c, then the rank of the new matrix is the same as the rank of A. 5. Elementary row operations do not change the rank of a matrix. 6. The rank of the product of two matrices is always equal to the smaller of the ranks of the individual matrices. 7. If the matrix B is obtained by interchanging two rows of the matrix A, then det B = det A. 8. If E is an elementary matrix, then det E = +1. 9. Every system of n linear equation in n unknowns can be solved by Cramer's Rule. 10. If A is a matrix with real entries and v is an eigenvector of A, then kv is an eigenvector of A for any real k.

True or False 1. If p locates a point on a line l in R and if n + 0 is normal to l, then any other point x on l must satisfy n • x = n • p. 2. A binary vector is a vector with two components which are integers modulo 2. 3. If A is invertible, then the only solution to Ax = b is A-'b. 4. If a row of a matrix A is multiplied by a scalar c, then the rank of the new matrix is the same as the rank of A. 5. Elementary row operations do not change the rank of a matrix. 6. The rank of the product of two matrices is always equal to the smaller of the ranks of the individual matrices. 7. If the matrix B is obtained by interchanging two rows of the matrix A, then det B = det A. 8. If E is an elementary matrix, then det E = +1. 9. Every system of n linear equation in n unknowns can be solved by Cramer's Rule. 10. If A is a matrix with real entries and v is an eigenvector of A, then kv is an eigenvector of A for any real k.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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