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MA 351 Ex 3 T/F

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Section 1

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(4.8a) Book

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Physics

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Mar 1, 2020

Cards (48)

Section 1

(48 cards)

(4.8a) Book

Front

False

Back

(4.8c)Book

Front

True

Back

(5.15) There is no matrix A that has the vectors X1 = [1,1,1]t, X2 =[1,0,1]t, and X3 = [2,1,2]t as eigenvectors corresponding, respectively, to the eigenvalues 1, 2, 3.

Front

True

Back

(4.3) Let A and B be 3 x 3 matrices. Then det(A + B) = det(A) + det(B).

Front

False

Back

(3.37) Let A be an m x n matric and let M be the matrix of Ta with respect to bases B and B^-. Then the row spaces of A and M are equal.

Front

False

Back

(3.36) Let A be an m x n matric and let M be the matrix of Ta with respect to bases B and B^-. Then the dimensions of row spaces of A and M are equal.

Front

True

Back

(4.12) Book

Front

True

Back

(5.10) Suppose that pa(lamda) = -(lamda)^3 (lamda - 2) (lamda + 3)^2. Then, the nullspace of A is at most two-dimensional.

Front

False

Back

(5.11) There is a 3 x 3 matrix with eigenvalues 1,2,3, and 4.

Front

False

Back

(3.4) It is impossible for a linear transformation from r2 into r2 to transform a parallelogram onto a line segment.

Front

False

Back

(5.2) There is no 3 x 3 matrix A with pa(lamda) = (lamda - 2)^2( lamda - 3).

Front

False

Back

(3.6) Suppose that T is a linear transformation of r2 into itself and I know what T transforms [1, 1]t and [2, 3]t to. Then, I can compute the effect of T on any vector.

Front

True

Back

(3.34) Let A be an m x n matrix and let M be the matrix of Ta with respect to bases B and B^-. Then the dimensions of the column spaces of A and M are equal.

Front

True

Back

(3.35) Let A be an m x n matric and let M be the matrix of Ta with respect to bases B and B^-. Then the column spaces of A and M are equal.

Front

False

Back

(3.32) Let B and B^- be ordered bases for R^n. Then the matrix of the identity transformation of R^n into itself with respect to B and B^- is the n x n identity matrix I.

Front

False

Back

(5.8) Suppose that A is a 3 x 3 matrix with 2 and 3 as its only eigenvalues. Then A is deficient.

Front

False

Back

(3.33) Let B nd B^- be ordered bases for R^n where B=B^-. Then the matrix of the identity transformation of R^n into itself with respect to B and B^- is the n x n identity matrix I.

Front

True

Back

(5.6) If X is an eigenvector for an n x n matrix A, then X is also an eigenvector for 2A.

Front

True

Back

(5.16) There is no matrix A that has the vectors X1 = [1,1,1]t, X2 =[1,0,1]t, and X3 = [2,1,3]t as eigenvectors corresponding, respectively, to the eigenvalues 1, 2, 3.

Front

False

Back

(4.10) Suppose that det(A + I) = 3, and det(A - I) = 5. Then det (A^2 - I) = 20.

Front

False

Back

(4.11) Suppose that det A = 2, det(A + I) = 3, and det(A + 2I) = 5. Then det(A^4 + 3A^3 + 2A^2) = 48.

Front

False

Back

(5.3c) If A is a 3 x 3 matrix with pa(lamda) = (2 -lamda)^2 (3 - lamda) then: (c) There are two linearly independent vectors X1 and X2 such that AXi = 2Xi

Front

False

Back

(4.5) Look at book

Front

False

Back

(5.3a) If A is a 3 x 3 matrix with pa(lamda) = (2 -lamda)^2 (3 - lamda) then: (a) There is a nonzero vector X such that AX = 2X.

Front

True

Back

(5.13) Suppose that A is a 3 x 3 diagonalizable matrix such that A^2 has eigenvalues 1, 4, and 9. Then A had eigenvalues 1, 2, and 3.

Front

False

Back

(3.38) Let A be an m x n matric and let M be the matrix of Ta with respect to bases B and B^-. Then the dimensions of the nullspaces of A and M are equal.

Front

True

Back

(4.6) Look at Book

Front

True

Back

(4.1) Look at book. It is solving the determinant.

Front

True

Back

(3.3) It is impossible for a linear transformation from r2 into r2 to transform a parallelogram onto square.

Front

False

Back

(4.8b) Book

Front

False

Back

(3.39) Let A be an m x n matric and let M be the matrix of Ta with respect to bases B and B^-. Then A and M have the same nullspace.

Front

False

Back

(4.9) Fall all n x n matrices A and B, det(AB) = det(BA).

Front

True

Back

(5.5) If X is an eigenvector for A with eigenvalue 3, then 2X is an eigenvector for A with eigenvalue 6.

Front

False

Back

(3.5) All transformations of r2 into r2 transform line segments onto line segments.

Front

False

Back

(3.2) It is impossible for a linear transformation from r2 into r 2 to transform a parallelogram onto a pentagon.

Front

True

Back

(5.9) The only nondeficient 3 x 3 matrix that has 1 as its only eigenvalue is the identity matrix. [hint: What us the dimension of the lamda = 1 eigenspace in this context]

Front

True

Back

(5.14) There are at least two 2 x 2 matrices, with eigenvectors Q1 = [1,2]t and Q2 = [-3,2]t corresponding to the respective eigenvalues lamda1 = -2 and lamda2 = 0.

Front

False

Back

(3.31) Let A be an m x n matrix and let M be the matrix of Ta with respect to bases B of R^m and B^- of R^n. Then rank A = rank M. [consider formula (3.36)]

Front

True

Back

(5.12) Suppose that A is a 3 x 3 matrix with eigenvalues 2, 3 ,and 4. Then det A = 9.

Front

False

Back

(5.1) If A is an n x n matrix that has zero for an eigenvalue, then A cannot be invertible.

Front

True

Back

(4.13) Book

Front

True

Back

(4.4) Look at book again

Front

True

Back

(5.3b) If A is a 3 x 3 matrix with pa(lamda) = (2 -lamda)^2 (3 - lamda) then: (b) Then there is at most one nonzero vector X such that AX = 3X.

Front

False

Back

(5.7) If 3 is an eigenvalue for A, then 9 is an eigenvalue for A^2.

Front

True

Back

(5.4) The sum of two eigenvectors is an eigenvector.

Front

False

Back

(3.1) A linear transformation of r2 into r2 transforms [1,2]t to [7,3]t and [3,4]t to [-1,1]t will also transform [5.8]t to [13,7]t.

Front

True

Back

(4.7)Look at Book

Front

True

Back

(4.2) Let A be a 3 x 3 matrix. Then det(5A) = 5det(A).

Front

False

Back