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![Given : o is a nxn matrix. Let A = [a[j] A= an nxn tie. a 12 an a23 Oาท ! ani anz an Onn nxn. Then rA=Tro ran rain ra13 rain](http://img.homeworklib.com/questions/8e76c010-811a-11eb-832c-ed6081c7e422.png?x-oss-process=image/resize,w_560)
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Find a formula for det(rA) when A is an nxn matrix. Choose the correct answer below....
Explain why the columns of an nxn matrix A are linearly independent when A is invertible...
Explain why the columns of an nxn matrix A are linearly independent when A is invertible Choose the correct answer below. O A. IFA is invertible, then for all x there is a b such that Ax=b. Since x = 0 is a solution of Ax0, the columns of A must be linearly independent OB. IA is invertible, then A has an inverse matrix A Since AA A AA must have linearly independent columns O C. If A is invertible,...
Let A and B be nxn matrices. Mark each statement true or false. Justify each answer....
Let A and B be nxn matrices. Mark each statement true or false. Justify each answer. Complete parts (a) through (d) below. a. The determinant of A is the product of the diagonal entries in A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The statement is false because the determinant of the 2x2 matrix A = is not equal to the product of the entries on the main...
Let A a b cd and let k be a scalar. Find a formula that relates...
Let A a b cd and let k be a scalar. Find a formula that relates det(A) to k and det(A) Find det(A) det(A)-(Simplify your answer.) Find det(A) det(k)=(Simpify your answer.) Use the preceding steps to find a formula for det(A). Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer.) O A. det[kA) = -det(A) OB. det/kA)= +det(A) O C. det/kA) - - det(A) OD. det/kA) - det(A)
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is...
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is the determinant of A. (b) If a 2 x 2 matrix satisfies tr(AP) = 5, tr(A) = 3, then find det(A). (The trace of a square matrix A, denoted by tr(A), is the sum of the elements on the main diagonal of A.
11. (1 pt) A and B are nxn matrices. Check the true statements below: A. The...
11. (1 pt) A and B are nxn matrices. Check the true statements below: A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)', where r is the number of row interchanges made during row reduction from A to U. B. If the columns of A are linearly dependent, then detA=0. • C. Adding a multiple of one row to another does not affect the determinant of a matrix....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 0 3 - 4 0 2 -4 -9 4 Choose the correct answer below. O A. The matrix is not invertible. If the given matrix is A, the equation Ax=b has at least one solution for each b in R3. OB. The matrix is invertible. The given matrix has 3 pivot positions. C. The matrix is invertible. The columns of the given matrix span...
[4 2. Explain why the columns of an nxn matrix A span R" when A is...
[4 2. Explain why the columns of an nxn matrix A span R" when A is invertible. Do not use any results from text section 2.3.
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 40 - 4 30 5 - 4 0 8 Choose the correct answer below O A. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution. O B. The matrix is invertible. The given matrix has 2 pivot positions. OC. The matrix is invertible. The columns of the given matrix span R. OD....
Let U and V be nxn orthogonal matrices. Explain why UV is an orthogonal matrix. [That...
Let U and V be nxn orthogonal matrices. Explain why UV is an orthogonal matrix. [That is, explain why UV is invertible and its inverse is (UV)'.] Why is UV invertible? O A. Since U and V are nxn matrices, each is invertible by the definition of invertible matrices. The product of two invertible matrices is also invertible. OB. UV is invertible because it is an orthogonal matrix, and all orthogonal matrices are invertible. O c. Since U and V...
Determine whether the given equation is separable, linear, neither, or both. ra dr do -703 Choose...
Determine whether the given equation is separable, linear, neither, or both. ra dr do -703 Choose the correct answer below. O A. The equation is separable. O B. The equation is linear. O C. The equation is neither separable nor linear. OD. The equation is both separable and linear.
Explain why the columns of an nxn matrix A are linearly independent when A is invertible Choose the correct answer below. O A. IFA is invertible, then for all x there is a b such that Ax=b. Since x = 0 is a solution of Ax0, the columns of A must be linearly independent OB. IA is invertible, then A has an inverse matrix A Since AA A AA must have linearly independent columns O C. If A is invertible,...
Let A and B be nxn matrices. Mark each statement true or false. Justify each answer. Complete parts (a) through (d) below. a. The determinant of A is the product of the diagonal entries in A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The statement is false because the determinant of the 2x2 matrix A = is not equal to the product of the entries on the main...
Let A a b cd and let k be a scalar. Find a formula that relates det(A) to k and det(A) Find det(A) det(A)-(Simplify your answer.) Find det(A) det(k)=(Simpify your answer.) Use the preceding steps to find a formula for det(A). Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer.) O A. det[kA) = -det(A) OB. det/kA)= +det(A) O C. det/kA) - - det(A) OD. det/kA) - det(A)
8. Let A be an nxn matrix with distinct n eigenvalues X1, 2... (a) What is the determinant of A. (b) If a 2 x 2 matrix satisfies tr(AP) = 5, tr(A) = 3, then find det(A). (The trace of a square matrix A, denoted by tr(A), is the sum of the elements on the main diagonal of A.
11. (1 pt) A and B are nxn matrices. Check the true statements below: A. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)', where r is the number of row interchanges made during row reduction from A to U. B. If the columns of A are linearly dependent, then detA=0. • C. Adding a multiple of one row to another does not affect the determinant of a matrix....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 0 3 - 4 0 2 -4 -9 4 Choose the correct answer below. O A. The matrix is not invertible. If the given matrix is A, the equation Ax=b has at least one solution for each b in R3. OB. The matrix is invertible. The given matrix has 3 pivot positions. C. The matrix is invertible. The columns of the given matrix span...
[4 2. Explain why the columns of an nxn matrix A span R" when A is invertible. Do not use any results from text section 2.3.
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 40 - 4 30 5 - 4 0 8 Choose the correct answer below O A. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution. O B. The matrix is invertible. The given matrix has 2 pivot positions. OC. The matrix is invertible. The columns of the given matrix span R. OD....
Let U and V be nxn orthogonal matrices. Explain why UV is an orthogonal matrix. [That is, explain why UV is invertible and its inverse is (UV)'.] Why is UV invertible? O A. Since U and V are nxn matrices, each is invertible by the definition of invertible matrices. The product of two invertible matrices is also invertible. OB. UV is invertible because it is an orthogonal matrix, and all orthogonal matrices are invertible. O c. Since U and V...
Determine whether the given equation is separable, linear, neither, or both. ra dr do -703 Choose the correct answer below. O A. The equation is separable. O B. The equation is linear. O C. The equation is neither separable nor linear. OD. The equation is both separable and linear.
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