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These are linear algebra problems. 1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is in...
a b с The matrix A= has a determinant of 6. d f g h 6...
a b с The matrix A= has a determinant of 6. d f g h 6 k (a) What is the determinant of the matrix B= 3d 29 -6f] За 2c -6b? 3h 2k -61 List the row & column 'operations' that were performed on A to produce B and state what each of these 'operations' does to the determinant. 3d (b) What is the determinant of the matrix C = 2a 39 2c 6k 3f 26 -6j -6h Explain...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T la +(-1) 6+2c +(-1)d - 1a + 2b + 0c + Od -3a + 56+ (-1) +0d 2a +(-2) b + 3c +0d] с d T-1 2) Let T(a + bx + cx+ dx?) = 1a + 2b + 1c +(-1)d la + 3b + 3c + Od 3a + 7b +6c+(-3) d 8a + 196 +16c+(-6) d 1-[]- 3) Let T 13a +(-17)...
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...
These are linear algebra problems. Let 5 1 7 0 0 -3 3 A= 5 1...
These are linear algebra problems.
Let 5 1 7 0 0 -3 3 A= 5 1 0 13 5 1 2 Find M23 and C23, M23 C23= Answer *1: exact number, no tolerance Answer *2: exact number, no tolerance Evaluate the determinant of the given matrix by reducing the matrix to row-echelon form. 2 -2 -6 6 -7 0 -2 -4 4 1 0 A = 4 0 0 2 0 0 0 3 .5 det(A)
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?...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
linear algebra 1 2. Let A be the 3 x 3 matrix: A= 3 3 0...
linear algebra
1 2. Let A be the 3 x 3 matrix: A= 3 3 0 -4 1-3 5 1 (a) Find det(A) by hand. (b) What can you say about the solution(s) to the linear system Az = ? A. No Solutions B. Unique Solution C. Infinitely Many Solutions (c) Is A invertible?
Note: We use u, v, w. etc. to denote u. v, w, etc. and R to...
Note: We use u, v, w. etc. to denote u. v, w, etc. and R to denote R. Question 1 a. Suppose Then find the value of g 2a) (h +2b) (i +2c) 3b За 2d 3c 2f b. Suppose A and B are n x n matrices with A invertible. Prove that det (A B) det B det A c. Suppose A is a 3 x 3 matrix such that det (A) - Find det d. Suppose A is...
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible =...
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible = det(A) 0 3 singular (non-invertible). For which value(s) of h is A = -2 -1 -4 Choose... Choose... 6 2 h-2 a 0,b 0,c+0,d +0 A = 4 -1 C 0 x-2 or x 4 For which values of x is A = invertible a 0,b 0,c 0,d=0 4 x 2 X#1 and x2...
Linear Algebra CS TIONARY 2 -11 6) Find the inverse of the matrix -4 -7 1...
Linear Algebra
CS TIONARY 2 -11 6) Find the inverse of the matrix -4 -7 1 4 -2 -6 if it exists. Show all work. No work, no credit. Use the algorithm we discussed in class. MIFFLIN COMPANY
a b с The matrix A= has a determinant of 6. d f g h 6 k (a) What is the determinant of the matrix B= 3d 29 -6f] За 2c -6b? 3h 2k -61 List the row & column 'operations' that were performed on A to produce B and state what each of these 'operations' does to the determinant. 3d (b) What is the determinant of the matrix C = 2a 39 2c 6k 3f 26 -6j -6h Explain...
Each transformation below is invertible. Determine the closed form representation for the inverse: 1) Let T la +(-1) 6+2c +(-1)d - 1a + 2b + 0c + Od -3a + 56+ (-1) +0d 2a +(-2) b + 3c +0d] с d T-1 2) Let T(a + bx + cx+ dx?) = 1a + 2b + 1c +(-1)d la + 3b + 3c + Od 3a + 7b +6c+(-3) d 8a + 196 +16c+(-6) d 1-[]- 3) Let T 13a +(-17)...
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...
These are linear algebra problems.
Let 5 1 7 0 0 -3 3 A= 5 1 0 13 5 1 2 Find M23 and C23, M23 C23= Answer *1: exact number, no tolerance Answer *2: exact number, no tolerance Evaluate the determinant of the given matrix by reducing the matrix to row-echelon form. 2 -2 -6 6 -7 0 -2 -4 4 1 0 A = 4 0 0 2 0 0 0 3 .5 det(A)
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?...
1. Algebra: Why are all these determinants zero? 3 -1 6 21 1 0 0 0 1 -2 3 -4 1 3 1 2 7 -1 2 2 1 3 5 2 3 4 5 (a) 1 1 1 1 1; (b) 2 5 2; (c) 3 0 1 -73 (d) 3 1 7 11 3 7 3 3 -1 6 21 5 2 6 10 3 3 3 3 2. Algebra: - la b c Given that d e...
linear algebra
1 2. Let A be the 3 x 3 matrix: A= 3 3 0 -4 1-3 5 1 (a) Find det(A) by hand. (b) What can you say about the solution(s) to the linear system Az = ? A. No Solutions B. Unique Solution C. Infinitely Many Solutions (c) Is A invertible?
Note: We use u, v, w. etc. to denote u. v, w, etc. and R to denote R. Question 1 a. Suppose Then find the value of g 2a) (h +2b) (i +2c) 3b За 2d 3c 2f b. Suppose A and B are n x n matrices with A invertible. Prove that det (A B) det B det A c. Suppose A is a 3 x 3 matrix such that det (A) - Find det d. Suppose A is...
For the following problems use: Annx n matrix A is invertible RREF(A) = I rank(A) - n A 2 x 2 matrix A is invertible = det(A) 0 3 singular (non-invertible). For which value(s) of h is A = -2 -1 -4 Choose... Choose... 6 2 h-2 a 0,b 0,c+0,d +0 A = 4 -1 C 0 x-2 or x 4 For which values of x is A = invertible a 0,b 0,c 0,d=0 4 x 2 X#1 and x2...
Linear Algebra
CS TIONARY 2 -11 6) Find the inverse of the matrix -4 -7 1 4 -2 -6 if it exists. Show all work. No work, no credit. Use the algorithm we discussed in class. MIFFLIN COMPANY
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