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QUESTION 3 1 points Which property of determinants is illustrated by the equation 8 8 l1...
Determine which property of determinants the equation illustrates. 1 3 2 0 0 0 96 -8...
Determine which property of determinants the equation illustrates. 1 3 2 0 0 0 96 -8 = 0 If one row of a matrix is a multiple of another row, then the determinant of the matrix is zero. If one row of a matrix consists entirely of zeros, then the determinant of the matrix is zero. If two columns of a matrix are interchanged, then the determinant of the matrix changes sign. If a row of a matrix is multiplied...
HW10P1 (14 points) For the following system of equations 2x1 x30 3x1 -x2 +4x3--8 4x 2...
HW10P1 (14 points) For the following system of equations 2x1 x30 3x1 -x2 +4x3--8 4x 2 2x5 a. b. c. d. e. (2 pts) write the linear system in the format, A X b. (2 pts) Find the determinant of the matrix A by using an expansion along row 1 (2 pts) Find the determinant of the matrix A by using an expansion along column 2. (2 pts) Find the determinant of the matrix A by using an expansion along...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A us...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
7. This question involves the concept of determinants and partitioned matrices. Historically, determinants first arose in...
7. This question involves the concept of determinants and partitioned matrices. Historically, determinants first arose in the context of solving systems of linear equations for one set of variables in terms of another. For example, if the coefficient matrix of the system u= ax + by v=cx + dy is invertible, then the equations can be solved for x and y in terms of u and v as au – cu 2= du - bv ad - bc y =...
Explain all parts of question 1 and question 2 in detail 1. Consider the matrix In...
Explain all parts of question 1 and question 2 in detail
1. Consider the matrix In + Inn, which has every diagonal entry equal to 2 and every off-diagonal entry equal to 1. (a) Compute det(In + Inn) for each of n = 1,2,3. (b) For n = 4, we have 2 1 1 1 1 2 1 1 1 1 2 1 111 2 2 1 1 1 -1 1 0 0 -1 0 1 0 -1 0 0...
Find a basis for the row space of A. 1 -1 3 2 -3 8 A-0...
Find a basis for the row space of A. 1 -1 3 2 -3 8 A-0 1 -2 Find a basis for the null space of A. Verify that every vector in row(A) is orthogonal to every vector in null(A). Need Help? Submit Answer Save Progress Practice Another Version 17. -12 points PooleLinAlg4 5.2.009. Find a basis for the column space of A. My Notes Ask Your Tea 1-1 3 5 2 1 A- 012 T. Find a basis for...
I need all details. Thx 2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has dete...
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
Problem: Matrix Implementation Create a class Matrix with the following method stubs for the following methods...
Problem: Matrix Implementation Create a class Matrix with the following method stubs for the following methods described: 1. read: reads in a matrix from the command line 2. display: prints the matrix to the command line 3. getRows: returns the number of rows 4. getCols: returns the number of columns 5. set: sets the double value at a particular column/row position 6. get: returns the value stored at a particular column/row position 7. Plus: returns a new Matrix object that...
QUESTION: PROVE THE FOLLOWING 4.3 THEOREM IN THE CASE r=1(no induction required, just use the definition of the determ...
QUESTION: PROVE THE FOLLOWING 4.3 THEOREM IN THE CASE
r=1(no induction required, just use the definition of the
determinants)
Theorem 4.3. The determinant of an n × n matrix is a linear function of each row when the remaining rows are held fixed. That is, for 1 Sr S n, we have ar-1 ar-1 ar-1 ar+1 ar+1 ar+1 an an rt whenever k is a scalar and u, v, and each a are row vectors in F". Proof. The proof...
2 invertible? C For which values of c is the matrix 8 O c 4 c...
2 invertible? C For which values of c is the matrix 8 O c 4 c =-4 Both of the above, i.e., c +4 Neither of the above, i.e., c +4. Suppose that the following row operations: interchange rows 1 and 3 multiply row 3 by 1/2 add -3 times row 1 to row 2 2 1 7 in this order, transform a matrix A into B = | 0 4-5 L0 0 3 What is the determinant of A?...
Determine which property of determinants the equation illustrates. 1 3 2 0 0 0 96 -8 = 0 If one row of a matrix is a multiple of another row, then the determinant of the matrix is zero. If one row of a matrix consists entirely of zeros, then the determinant of the matrix is zero. If two columns of a matrix are interchanged, then the determinant of the matrix changes sign. If a row of a matrix is multiplied...
HW10P1 (14 points) For the following system of equations 2x1 x30 3x1 -x2 +4x3--8 4x 2 2x5 a. b. c. d. e. (2 pts) write the linear system in the format, A X b. (2 pts) Find the determinant of the matrix A by using an expansion along row 1 (2 pts) Find the determinant of the matrix A by using an expansion along column 2. (2 pts) Find the determinant of the matrix A by using an expansion along...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
7. This question involves the concept of determinants and partitioned matrices. Historically, determinants first arose in the context of solving systems of linear equations for one set of variables in terms of another. For example, if the coefficient matrix of the system u= ax + by v=cx + dy is invertible, then the equations can be solved for x and y in terms of u and v as au – cu 2= du - bv ad - bc y =...
Explain all parts of question 1 and question 2 in detail
1. Consider the matrix In + Inn, which has every diagonal entry equal to 2 and every off-diagonal entry equal to 1. (a) Compute det(In + Inn) for each of n = 1,2,3. (b) For n = 4, we have 2 1 1 1 1 2 1 1 1 1 2 1 111 2 2 1 1 1 -1 1 0 0 -1 0 1 0 -1 0 0...
Find a basis for the row space of A. 1 -1 3 2 -3 8 A-0 1 -2 Find a basis for the null space of A. Verify that every vector in row(A) is orthogonal to every vector in null(A). Need Help? Submit Answer Save Progress Practice Another Version 17. -12 points PooleLinAlg4 5.2.009. Find a basis for the column space of A. My Notes Ask Your Tea 1-1 3 5 2 1 A- 012 T. Find a basis for...
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
QUESTION: PROVE THE FOLLOWING 4.3 THEOREM IN THE CASE
r=1(no induction required, just use the definition of the
determinants)
Theorem 4.3. The determinant of an n × n matrix is a linear function of each row when the remaining rows are held fixed. That is, for 1 Sr S n, we have ar-1 ar-1 ar-1 ar+1 ar+1 ar+1 an an rt whenever k is a scalar and u, v, and each a are row vectors in F". Proof. The proof...
2 invertible? C For which values of c is the matrix 8 O c 4 c =-4 Both of the above, i.e., c +4 Neither of the above, i.e., c +4. Suppose that the following row operations: interchange rows 1 and 3 multiply row 3 by 1/2 add -3 times row 1 to row 2 2 1 7 in this order, transform a matrix A into B = | 0 4-5 L0 0 3 What is the determinant of A?...
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