For the following matrices, find the dimension of Row space, Column space and Null space. (a) Let A be the 4 x 4 identity matrix, then Dim Row (A): Number Dim Col (A): Number (b) Let B be the 5 x 5 zero matrix, then Dim Row (B): Number Dim Col (B): Number (c) Let C be the 4 x 7 matrix with 1 in every position, then Dim Row (C): 1 Dim Col (C): 1 Dim Nul (A): Number Dim Nul (B): Number Dim Nul (C): Number (d) Let D be the 4 x 2 matrix with 2 in every position in the top row, and 1 everywhere else, then Dim Row (D): 1 Dim Col (D): 1 Dim Nul (D): 1 (e) Let E be the 4 x 5 matrix with 1 in every position in the first column, and -1 everywhere else, then Dim Row (E): 1 Dim Col (E): 1 Dim Nul (E): Number (f) Let F be the 5 x 5 matrix with 1 in every position below the main diagonal, and zeros on and above the diagonal, then Dim Row (F): Number Dim Col (F): Number Dim Nul (F): Number Give a vector that spans Nul(F). Enter in the form [1, 2, 3, 4, 5]
For the following matrices, find the dimension of Row space, Column space and Null space. (a) Let A be the 4 x 4 identity matrix, then Dim Row (A): Number Dim Col (A): Number (b) Let B be the 5 x 5 zero matrix, then Dim Row (B): Number Dim Col (B): Number (c) Let C be the 4 x 7 matrix with 1 in every position, then Dim Row (C): 1 Dim Col (C): 1 Dim Nul (A): Number Dim Nul (B): Number Dim Nul (C): Number (d) Let D be the 4 x 2 matrix with 2 in every position in the top row, and 1 everywhere else, then Dim Row (D): 1 Dim Col (D): 1 Dim Nul (D): 1 (e) Let E be the 4 x 5 matrix with 1 in every position in the first column, and -1 everywhere else, then Dim Row (E): 1 Dim Col (E): 1 Dim Nul (E): Number (f) Let F be the 5 x 5 matrix with 1 in every position below the main diagonal, and zeros on and above the diagonal, then Dim Row (F): Number Dim Col (F): Number Dim Nul (F): Number Give a vector that spans Nul(F). Enter in the form [1, 2, 3, 4, 5]
Algebra and Trigonometry (6th Edition)
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![For the following matrices, find the dimension of Row space, Column space and Null space.
(a) Let A be the 4 x 4 identity matrix, then
Dim Row (A): Number Dim Col (A): Number
(b) Let B be the 5 x 5 zero matrix, then
Dim Row (B): Number
Dim Col (B): Number
(c) Let C' be the 4 x 7 matrix with 1 in every position, then
Dim Row (C): 1
Dim Col (C): 1
Dim Nul (A): Number
Dim Nul (B): Number
Dim Nul (C): Number
(d) Let D be the 4 x 2 matrix with 2 in every position in the top row, and 1 everywhere else, then
Dim Row (D): 1
Dim Col (D): 1
Dim Nul (D): 1
(e) Let E be the 4 x 5 matrix with 1 in every position in the first column, and -1 everywhere else, then
Dim Row (E): 1
Dim Col (E): 1
Dim Nul (E): Number
(f) Let ♬ be the 5 x 5 matrix with 1 in every position below the main diagonal, and zeros on and above the diagonal, then
Dim Row (F): Number
Dim Col (F): Number
Dim Nul (F): Number
Give a vector that spans Nul(F). Enter in the form [1, 2, 3, 4, 5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ac09755-9639-4075-b6f1-d2ae73f82d81%2F9af7a1bb-b53b-4b2e-b517-0e3c7dec8c99%2Fhqrp9f_processed.png&w=3840&q=75)
Transcribed Image Text:For the following matrices, find the dimension of Row space, Column space and Null space.
(a) Let A be the 4 x 4 identity matrix, then
Dim Row (A): Number Dim Col (A): Number
(b) Let B be the 5 x 5 zero matrix, then
Dim Row (B): Number
Dim Col (B): Number
(c) Let C' be the 4 x 7 matrix with 1 in every position, then
Dim Row (C): 1
Dim Col (C): 1
Dim Nul (A): Number
Dim Nul (B): Number
Dim Nul (C): Number
(d) Let D be the 4 x 2 matrix with 2 in every position in the top row, and 1 everywhere else, then
Dim Row (D): 1
Dim Col (D): 1
Dim Nul (D): 1
(e) Let E be the 4 x 5 matrix with 1 in every position in the first column, and -1 everywhere else, then
Dim Row (E): 1
Dim Col (E): 1
Dim Nul (E): Number
(f) Let ♬ be the 5 x 5 matrix with 1 in every position below the main diagonal, and zeros on and above the diagonal, then
Dim Row (F): Number
Dim Col (F): Number
Dim Nul (F): Number
Give a vector that spans Nul(F). Enter in the form [1, 2, 3, 4, 5]
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VIEWStep 2: Find the dimension of Row, column and Null space of A when it is 4X4 identity matrix
VIEWStep 3: Find the dimension of Row, column and Null space of B when it is 5X5 zero matrix
VIEWStep 4: Find the dimension of Row, column and Null space of C when it is 4X7 matrix with 1 in every position
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