Consider matrix A = scalar product w. y. 0 (₁2) and vectors x = (2) and y = (1) . Calculate matrix B= (A - AT)² and vector w = Bx. Then, evaluate the

Q: Calculate the scalar triple product u (vx w), where u = . (Use symbolic notation and fractions where…

A: Here we have to evaluate the scalar triple product u. (v x w) .

Q: 3. Solve the system below using the specified method. Write your answer in vector form. X1 - 3x2 = 2…

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Q: Verify that (AB)T = BTAT.

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Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 2i + 9j – 4k. (a) U X V (b) (c) v x v

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Q: 1. Consider the matrices A = G ), B = (,) and C= (-1 0 5) (a) Evaluate (AB)C and A(BC). Check that…

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Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

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Q: Solve for the matrix X eMz (R): -2 3 ļ s X = 7|o

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Q: 2 =(², 2). (a) Find the inverse of the matrix A = (b) Find the direct product of the matrices A = =…

A: (a) The given matrix is A=21-12 (b) The given matrices are A=1302, B=12-12 (c) The given matrix is…

Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 6i + 9j - 5k. (a) u xv (b) vxu (c) vxv

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Q: How to get Linear equations from matrices ?

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Q: Find u x v, v x u, and v x v. u = 4i + 7k v = 6i + 9j - 5k. (a) ux v (b) (c) V x u V X V

A: We have given two vectors u and v and we want to find the cross product of the given vectors in…

Q: Express in the form of x + iy: 6-7i (i) 5+i 1 + (3+i)2 1 (ii) (3-i)2

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Q: -1 – 7 -3 (a) Let A = 15 6 Find the second column of A-1 without com- 1 3 puting the other columns.

A: Given,A=-1-7-32156132

Q: [1 3 A = 0 2 2 2 l2 1 1.

A: given matrix is                                                A=131022211 we have to find inverse…

Q: Find u x v, v x u, and v x v. u = (3, -3, -1) v = (-2, –7, -5) (a) ux v

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Q: Find u v, 2(u + 3v), and 2v- u. - u = (6, -5, 8, 3), (a) u-v= (b) 2(u +3v) = (c) 2v - u = v = (-2, 5…

A: The solution is shown below-

Q: Solve using matrices. 7x+6y = 32, 13. -x+8y = 22

A: We can solve the given equation by using augmented matrix.

Q: stitution? I have to use the Column Correspon

A: Is (1,2,3,4,5,6)∈ span( (1,1,1,1,1,1),(0,1,0,1,0,2),(6,5,4,3,2,1)) > A x1 x2 x3 x4 x5 x6…

Q: (a) If j² = -1, simplify

A: (a) if j2=-1, then      (i) j6=

Q: m(z + 3i) = 6

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Q: Diagonalized  if possible, where is A=[■(4&0&1@1&1&0@3&0&1)].

A: Given A =   4 0 1     1 1 0     3 0 1

Q: Consider the three equations: x - 2y = -1,3x4z = -1 and 2x +2y+z=2. Write these in the form of Ax =…

A: Given equations x - 2y = -1 3x - 4z = -12x + 2y + z = 2

Q: Find |A|, [B], A + B, and JA + BỊ. Then verify that |A| + |B| = |A + BỊ. 1 7 A = 1 -1 0 0 1 -1 B = 7…

A: We can solve this as follows:

Q: Let u = (−3,2,1,0), v = (4,7,−3,2), and w = (5, −2, 8, 1). Find the components of −u+(v−4w)

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Q: Write equations 3.x – 4y = 7 and 2x + y = 1 as the matrix equation - A() - (1)- and then: Calculate…

A: given equations;  3x-4y=7--------(1) 2x+y=1---------(2) now we formulate the equation as follows A=…

Q: 2. Write the matrix equation 1 -2 -3 1 2 -3 1 3-4 = X4 as a vector equation. You do not need to…

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Q: Write the row vectors and the column vectors of the matrix. -3 1 [8 -2] 0 (a) the row vectors -3 0 1…

A: Given matrixThe horizontal elements in a matrix called elements of row vectorsThe vertical elements…

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v