1. Each statement in Theorem 3 is true when the word row is replaced everywhere
ID: 2939954 • Letter: 1
Question
1. Each statement in Theorem 3 is true when the wordrow is replaced everywhere by the word column.True or False? Theorem 3 a. if a multiple of one row of A is added to another row toproduce a matrix B, then det B = det A. b. if two rows of A are interchanged to produce B, thendet B = -detA. c. if one row of A is multiplied by k to produce B, thendet B = k*detA. 2.The determinant of an invertible matrix A is ______the product of the pivots in an echelon form U ofA, multiplied by (-1)r, wherer is the number of row interchanges made during rowreduction from A to U. a. always b. sometimes c. never 3. A row replacement operation on a matrix ______changes the value of the determinant. a. always b. sometimes c. never 1. Each statement in Theorem 3 is true when the wordrow is replaced everywhere by the word column.True or False? Theorem 3 a. if a multiple of one row of A is added to another row toproduce a matrix B, then det B = det A. b. if two rows of A are interchanged to produce B, thendet B = -detA. c. if one row of A is multiplied by k to produce B, thendet B = k*detA. 2.The determinant of an invertible matrix A is ______the product of the pivots in an echelon form U ofA, multiplied by (-1)r, wherer is the number of row interchanges made during rowreduction from A to U. a. always b. sometimes c. never 3. A row replacement operation on a matrix ______changes the value of the determinant. a. always b. sometimes c. neverExplanation / Answer
QuestionDetails: 1. Each statement in Theorem 3 is true when the wordrow is replaced everywhere by the wordcolumn.True or False? Theorem 3 a. if a multiple of one row of A is added to another row toproduce a matrix B, then det B = det A.
TRUE
b. if two rows of A are interchanged to produce B, thendet B = -detA....
TRUE c. if one row of A is multiplied by k to produce B, thendet B = k*detA.
TRUE
2.The determinant of an invertible matrix A is ______the product of the pivots in an echelon
form U of A, multiplied by(-1)r, where r is the number of rowinterchanges made during
row reduction from A to U.
TRUE ...FOR ROW TRANSFORMATION
THE SAME TERMINOLOGY IS NOT USED FOR COLUMN TRANSFORMATION
ROW ECHELON TRANSFORMATION REFERS TO ROWS ONLY NOT COLUMNS.
a. always ????? WHAT IS THIS ?
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