4. (a) Which matrix corresponds to the row operation that replaces with ? (b)  
4.
(a) Which 
matrix 
corresponds to the row
operation that replaces 
with 
?
(b) Find the inverse of
. Justify your answer in
terms of row operations.
Homework Answers
Add Answer to:
4.
(a) Which matrix corresponds to the row
operation that replaces with ?
(b)  
5. Suppose L is a unit-lower-triangular matrix. (a) What can you say about the reduced row...
5. Suppose L is a unit-lower-triangular matrix. (a) What can you say about the reduced row echelon form R of L? Be as specific as possible. (b) If you perform the elementary row operations on I that are used to transform L to R, what matrix do you get? Write your answer in terms of I, R, and/or L and basic matrix operations (addition, multiplication, transpose, inverse, etc.). (c) If you perform the same elementary row operations to a matrix...
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT....
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
Perform the following matrix operation. Enter your matrix by row, with entries separated by commas. would...
Perform the following matrix operation. Enter your matrix by row, with entries separated by commas. would be entered as a,b,c,d. 49cdan Do not round your answers. st Save Submit Problem #4 for Grading Attempt #1 | Attempt #2 Attempt #3 Problem #4 Your Answer: Your Mark: Perform the following matrix operation. [1 212 2:] Enter your matrix by row, with entries separated by commas. uld be entered as a,b,c,d,e,f
Perform the following matrix row operation and write the new matrix. [ 2 -6 10 14...
Perform the following matrix row operation and write the new matrix. [ 2 -6 10 14 5 7-6 110-7-5 After performing the row operation, the new matrix is DOO (Simplify your answer.) Enter your answer in the edit fields and then click Check Answer.
Find the inverse of the matrix using row operations: 1 4 -1 1 A= -1 2...
Find the inverse of the matrix using row operations: 1 4 -1 1 A= -1 2 -3 6 -1
「 : / (2) Let A- be an arbitrary 2 x 2 matrix. (a) If A is invertible, perform row operations to...
「 : / (2) Let A- be an arbitrary 2 x 2 matrix. (a) If A is invertible, perform row operations to determine a row echelon form of A. (Hint: You may need to consider different cases, e.g., when a-0 and when a f 0.) (b) Under certain conditions, we can row reduce [A | 2 to [| B] where d -b ad- be-a Use the row echelon form of A from part (a) to find conditions under which the...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: X1 + 2yı - 2 = 5 4x+9y, - 32 = 8 (5x + 12yı - 324 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down within...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2y, - 2 = 5 4x1 +9y1 - 32 = 8 (5x + 12y - 321 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above,...
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
5. Suppose L is a unit-lower-triangular matrix. (a) What can you say about the reduced row echelon form R of L? Be as specific as possible. (b) If you perform the elementary row operations on I that are used to transform L to R, what matrix do you get? Write your answer in terms of I, R, and/or L and basic matrix operations (addition, multiplication, transpose, inverse, etc.). (c) If you perform the same elementary row operations to a matrix...
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
Perform the following matrix operation. Enter your matrix by row, with entries separated by commas. would be entered as a,b,c,d. 49cdan Do not round your answers. st Save Submit Problem #4 for Grading Attempt #1 | Attempt #2 Attempt #3 Problem #4 Your Answer: Your Mark: Perform the following matrix operation. [1 212 2:] Enter your matrix by row, with entries separated by commas. uld be entered as a,b,c,d,e,f
Perform the following matrix row operation and write the new matrix. [ 2 -6 10 14 5 7-6 110-7-5 After performing the row operation, the new matrix is DOO (Simplify your answer.) Enter your answer in the edit fields and then click Check Answer.
Find the inverse of the matrix using row operations: 1 4 -1 1 A= -1 2 -3 6 -1
「 : / (2) Let A- be an arbitrary 2 x 2 matrix. (a) If A is invertible, perform row operations to determine a row echelon form of A. (Hint: You may need to consider different cases, e.g., when a-0 and when a f 0.) (b) Under certain conditions, we can row reduce [A | 2 to [| B] where d -b ad- be-a Use the row echelon form of A from part (a) to find conditions under which the...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: X1 + 2yı - 2 = 5 4x+9y, - 32 = 8 (5x + 12yı - 324 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down within...
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2y, - 2 = 5 4x1 +9y1 - 32 = 8 (5x + 12y - 321 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
(1 point) Consider the matrix -5 7 8-9 20 -30 8-3 -15 -19 9 -4 10-11 5-8 (a) On the matrix above, perform the row operation R1 15 R1 . The new matrix is: (b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations () R3 R3 15R1, (iii) R4→R4+10R1. The new matrix is: (c) Using the matrix obtained in your answer for part (b) as the initial matrix, next...
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