TRUE OR FALSE 27. For any matrices A and B for which the product AB isdefined, the (-entry of AB equals gu bi-28. For any matrices A and B for which the product AB isdefined, the ()-entry of AB equals the sum of the productsof corresponding entries from the ith column of Á and theith row of B.29. If A, B, and C are matrices for which the product A(BC) isdefined, then A(BC) = (AB)C.30. If A and B are m × n matrices and Cis an nx p matrix, then(A + B)C = AB + BC.31. If A and B are n x n matrices, then the diagonal entries ofthe product matrix AB are aibua2b,.dakan32. If the product AB is defined and either A or B is a zeromatrix, then AB is a zero matrix.33. If the product AB is defined and AB is a zero matrix, theneither A or B is a zero matrix.34. If Aa and Ap are both 2 x 2 rotation matrices, then A„Ap is a|2 x 2 rotation matrix.35. The product of two diagonal matrices is a diagonal matrix.36. In a symmetric n × n matrix, the ()- and (iD-entries areequal for all i = 1,2,.n and j = 1,2,.n.37. The determinant of a matrix is a matrix ofthe same size.b= ad + bea38. det39. If the determinant of a 2 x 2 matrix equals zero, then thematrix is invertible.40. If a 2 x 2 matrix is invertible, then its determinant equalszero.41. If B is a matrix obtained by multiplying each entry of somerow of a 2 x 2 matrix A by the scalar k, then detB = k det4.

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27. For any matrices A and B for which the product AB is defined, the (L0-entry of AB equals a bu

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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TRUE OR FALSE

27. For any matrices A and B for which the product AB is
defined, the (-entry of AB equals gu bi-
28. For any matrices A and B for which the product AB is
defined, the ()-entry of AB equals the sum of the products
of corresponding entries from the ith column of Á and the
ith row of B.
29. If A, B, and C are matrices for which the product A(BC) is
defined, then A(BC) = (AB)C.
30. If A and B are m × n matrices and Cis an nx p matrix, then
(A + B)C = AB + BC.
31. If A and B are n x n matrices, then the diagonal entries of
the product matrix AB are aibua2b,.dakan
32. If the product AB is defined and either A or B is a zero
matrix, then AB is a zero matrix.
33. If the product AB is defined and AB is a zero matrix, then
either A or B is a zero matrix.
34. If Aa and Ap are both 2 x 2 rotation matrices, then A„Ap is a|
2 x 2 rotation matrix.
35. The product of two diagonal matrices is a diagonal matrix.
36. In a symmetric n × n matrix, the ()- and (iD-entries are
equal for all i = 1,2,.n and j = 1,2,.n.
37
. The determinant of a matrix is a matrix of
the same size.
b
= ad + be
a
38. det
39. If the determinant of a 2 x 2 matrix equals zero, then the
matrix is invertible.
40. If a 2 x 2 matrix is invertible, then its determinant equals
zero.
41. If B is a matrix obtained by multiplying each entry of some
row of a 2 x 2 matrix A by the scalar k, then detB = k det4.

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