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+ y +z- 0 y-1 5. Solve: ANS: -(2) -(0) 6. Suppose: W Calculate and H...
3 y+ z 0 2. Let W be a plane characterized by the equation W. D...
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the orthogonal projection of R onto W 2) Find the distance between a vector (2, 2, 15) and the plane W. (5 (3
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the...
2 -3 3 (a) Write the system, not the augmented matrix, that correspond to the matrix...
2 -3 3 (a) Write the system, not the augmented matrix, that correspond to the matrix equation Axw (b) Solve the system Ax w. Show your work. (c) Write the vector w as a linear combination of the columns of A R3. Explain (d) Let {a, a2, as) be the colulins of A. Is Span {a, a2, аз}
2,3, 6, 7 1. Without matrices, solve the following system using the Gaussian elimination method +...
2,3, 6, 7
1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size...
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size of AB is: b) If C is a 3×4 matrix and size of DC is 2×4 matrix , then size of D is: c) True or False: If A and B are both 3 × 3 then AB = BA d) The 2 × 2 identity matrix is: I = e) Shade the region 3x + 2y > 6. f) Write the augmented matrix...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) i...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
1 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns...
1 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns of A by ay, az, az, and let W= = Span{a,,a,,az}. -34 2 -5 1 a. Is b in {a4, az, az}? How many vectors are in {aq,a2, az}? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {aq, az, az}? No Yes How many vectors...
1 7 -6 13 Given A and b to the right, write the augmented matrix for...
1 7 -6 13 Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. A= -2 -5 3 b= -8 ܗ - 4 - 6 -2 Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Select the correct choice below and fill in any answer boxes within...
5. (15 pts) For the linear system x + 2y + z = 4 2 +...
5. (15 pts) For the linear system x + 2y + z = 4 2 + 5y + 2z = 3 4x - y +9z = -1 a) Write the system in matrix-vector form Ax = b. b) Form the augmented matrix [ A6] c) Fill-in the necessary row operations to produce each of the following matrices. 4 1 2 1 0 -3 -1 0 9 -5 17 → O CON 1 00-8 4 -1 20 1 2 1 4...
Use the augmented matrix A = 1 3 6 10 0 0 1 olo 0 0...
Use the augmented matrix A = 1 3 6 10 0 0 1 olo 0 0 0 0 0 0 0 0 0 0 far 1. Circle the pivots in the matrix A 2. Write the system of equations represented by A. 3. Identify each variable you used in the system as either basic or free. 4. Express the set of all solutions to the system of equations from (2) as a single vector. 5. Will the solution set be...
12х + 18у — 4z. (1 point) Let x, y, z be (non-zero) vectors and suppose...
12х + 18у — 4z. (1 point) Let x, y, z be (non-zero) vectors and suppose w = If z 2x 3y, then W = X+ у. Using the calculation above, mark the statements below that must be true. |A. Span(w, x) Span(w, z) B. Span(w, y) Span(w, y, z) |C. Spanx, y, z) = Span(x, y) D. Span(w, z) Span(x, y) E. Span(w, x, z) = Span(w, x, y)
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the orthogonal projection of R onto W 2) Find the distance between a vector (2, 2, 15) and the plane W. (5 (3
3 y+ z 0 2. Let W be a plane characterized by the equation W. D (5 Find an orthonormal basis for (57) Find the standard matrix for the...
2 -3 3 (a) Write the system, not the augmented matrix, that correspond to the matrix equation Axw (b) Solve the system Ax w. Show your work. (c) Write the vector w as a linear combination of the columns of A R3. Explain (d) Let {a, a2, as) be the colulins of A. Is Span {a, a2, аз}
2,3, 6, 7
1. Without matrices, solve the following system using the Gaussian elimination method + 1 + HP 6x - Sy- -2 2. Consider the following linear system of equation 3x 2 Sy- (a) Write the augmented matrix for this linear system (b) Use row operations to transform the augmented matrix into row.echelon form (label all steps) (c) Use back substitution to solve the linear system. (find x and y) x + 2y 2x = 5 3. Consider the...
e 09, 201 (6) 2 points An equation for the level curve of f(z, y) = In(z+y) that passes through the point (0, e2) is A. z + y = e2 B. I+y e C. z+y 3. D. None of the above (7) 2 points The gradient of f(z,y, z) = ep at the point (-1,-1,2) is A. (2e2,e2,2e2). B. (-e,-e,2e2). C. (-2e2,-2e2, e) D. (-2e2,-e,-e) (8) 2 points Let f be a function defined and continuous, with continuous first...
1 O -7 5 Let A= 0 2 -2 and b= - 1 Denote the columns of A by ay, az, az, and let W= = Span{a,,a,,az}. -34 2 -5 1 a. Is b in {a4, az, az}? How many vectors are in {aq,a2, az}? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] a. Is b in {aq, az, az}? No Yes How many vectors...
1 7 -6 13 Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. A= -2 -5 3 b= -8 ܗ - 4 - 6 -2 Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Select the correct choice below and fill in any answer boxes within...
5. (15 pts) For the linear system x + 2y + z = 4 2 + 5y + 2z = 3 4x - y +9z = -1 a) Write the system in matrix-vector form Ax = b. b) Form the augmented matrix [ A6] c) Fill-in the necessary row operations to produce each of the following matrices. 4 1 2 1 0 -3 -1 0 9 -5 17 → O CON 1 00-8 4 -1 20 1 2 1 4...
Use the augmented matrix A = 1 3 6 10 0 0 1 olo 0 0 0 0 0 0 0 0 0 0 far 1. Circle the pivots in the matrix A 2. Write the system of equations represented by A. 3. Identify each variable you used in the system as either basic or free. 4. Express the set of all solutions to the system of equations from (2) as a single vector. 5. Will the solution set be...
12х + 18у — 4z. (1 point) Let x, y, z be (non-zero) vectors and suppose w = If z 2x 3y, then W = X+ у. Using the calculation above, mark the statements below that must be true. |A. Span(w, x) Span(w, z) B. Span(w, y) Span(w, y, z) |C. Spanx, y, z) = Span(x, y) D. Span(w, z) Span(x, y) E. Span(w, x, z) = Span(w, x, y)
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