Determine whether the statement are TRUE or FALSE. Write TRUE if the Statement is True and False otherwise. 36. In a symmetric n x n matrix, the (i,j)- and (j, i)-entriesare 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.а38. det= ad + bc.39. 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 ofsome row of a 2 × 2 matrix A by the scalar k, thendet B = k det A.42. For n > 2, the (i,j)-cofactor of an n x n matrix A is thedeterminant of the (n – 1) × (n – 1) matrix obtained bydeleting row i and column j from A.43. For n > 2, the (i,j)-cofactor of an n x n matrix A equals(-1)i+j times the determinant of the (n – 1) × (n – 1)matrix obtained by deleting row i and column j from A.44. The determinant of an n x n matrix can be evaluated bya cofactor expansion along any row.45. Cofactor expansion is an efficient method for evaluatingthe determinant of a matrix.46. The determinant of a matrix with integer entries must bean integer. 47. The determinant of a matrix with positive entries must bepositive.48. If some row of a square matrix consists only of zeroentries, then the determinant of the matrix equals zero.49. An upper triangular matrix must be square.50. A matrix in which all the entries to the left and belowthe diagonal entries equal zero is called a lower triangularmatrix.51. A 4 x 4 upper triangular matrix has at most 10 nonzeroentries.52. The transpose of a lower triangular matrix is an uppertriangular matrix.53. The determinant of an upper triangular n x n matrix or alower triangular n xn matrix equals the sum of its diag-onal entries.54. The determinant of I, equals 1.

Answered: 36. In a symmetric n x n matrix, the…

36. In a symmetric n x n matrix, the (i,j)- and (j, i)-entries are equal for all i = 1,2,.n and j = 1,2,.,n.

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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