let a₁, a2 and a3 be the columns of A, let B = {a1, a2, a3} and let H = span(B).

Q: let v = (1, 3, −2) and w = (2, −1, 4). Compute v × w.

A:

Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

A:

Q: 12. Circle all the matrix products that ARE possible a. A3x4 B4x3 b. A2x2 B2x2 С. A4x1 B1x1 D. A2x3…

A:

Q: Calculate v x w: v = (5,6,2), V X W W = (5, 4, 7)

A: Step 1: Step 2: Step 3: Step 4:

Q: What are free columns?

A: A matrix is a rectangular array containing the set of numbers arranged in rows and columns. A matrix…

Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: Let A be a 4×5 matrix with 4 pivots. Do the columns of A span R4? Do they span R5? Justify your…

A: As A is a 4 x 5 matrix with 4 pivots so, it has a pivot in its every row. So, yes the columns of A…

Q: a) Find all such that . b) If is a zero-one matrix, find. b) Find the inverse of the encrypting…

A: Clear explanation is given below find the answer below

Q: Let i = (2, –1, 5) and ū = (5, –7,3). Find 37 – 5ū. %3D - А. (-19, —32, 0) В. (-19, 32, 0) С. (19,…

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Q: 1 Let the matrix A= Find A2 5A + 312x2. - Select one: a.

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Q: Calculate the area of the parallelogram determined by the points (-1 , -1), (2 , 4), (4 , 3) and (7…

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Q: Let U=(-4, 3, 3) and V=(2, 1, 1). Find (2U+V), *. | (then find | (2U+V

A: Find 2U+V and it's magnitude.

Q: Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.

A:

Q: Let a,b, and c be distinct real numbers, and * be any real number. Determine if the empty blank…

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Q: Let a and b be integers. (a) Show that b is a linear combination of a + 3b and a + 2b. (b) Show that…

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Q: Consider the following linear equations: -6x + 3y + 6z -6x + (16-k)y + 5z -6x + 3y + (8 - k)z a) -6…

A:

Q: Express Ac as a linear combination of the columns of A.

A: Given A=2-34-1235-1-2   C=214

Q: Let A and B be two matrices innRREF , if they are row equivalent then A=B.

A:

Q: Let u = (1, 2, 3), v = (4, 4, -2), and w = (6, -1, -2). Find z, where 2u + v – w + 3z = 0. z =

A:

Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A: According to the given information, it is required to find a linear dependence between the columns…

Q: if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

A: (A|b) is the augmented matrix formed by placing elements of matrix B to the right of elements of…

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: Let B be a 5 x 5 matrix such that each row of B contains every number from the following list…

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Q: = x° + y*, ¤ = + u, and y = v – u². Find Your answer should be in terms of r, y, u, and v. dv

A:

Q: V=(2,7,10),V%=(1,2,3), Vz (1,3,5),Vz=(1,5,9)

A: Let V=aV1+bV2 +cV3 where a, b and c are constants.

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

A:

Q: Use the

A: we have; 3x1-2x2+4x3=213x1+4x2-2x3=92x1-x2-x3=10

Q: 4 03 -2 3 0 10 5 a. 1 7 b. -3 7 0 c.-3 9 0 051 7 0

A: (a) The given matrix is 105017 Let S be the set of columns vector then we have  S=(1,0), (0,1),…

Q: If a 6 x 6 matrix contains 19 zeros, show that there are 4 zeros which are all in distinct rows and…

A: A 6x6 matrix has 36 entries. Given if a 6x6 matrix contains 19 zeros, then to show that there are 4…

Q: Perform the indicated matrix operations:

A: -4  3  7-6+6-32-4

Q: Let A be the 3×3 matrix of zeros. Describe all solutions to Ax​=0.

A: