3) Let T d b }]= la + 1b + 1c + 5d + 2e +2f la + 2b + 0c + 5d + 3e + 1f 3a + 4b +3c + 17d+ 8e +6f -2a + (-1) b+ (-4) c+ (-12) d + (-3) e+ (-6) f] i) A basis for Range(T) would be: ii) The Range of this transformation spans the entire codomain:

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: Draw vector 1/2CD - 2FE

A:

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

A:

Q: Given'! I1xl1= 3 Ily 1 X.Y--2 (x-2y) (3x +5y) Sol: 3(4) + 2- 10 19

A: Given:       x=3, y=1, x·y=-2  To find:          x-2y·3x+5y       =x·3x+5y-2y·3x+5y…

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

A:

Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

A: We know that a set of vectors u1, u2, ……, un is said to be linearly independent if the equation…

Q: Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a…

A: Ggg

Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

A:

Q: y Suppose E (A, B) is controllable. Suppose a change of basis is performed so that we obtain a new…

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Q: If the set {(1,2, 1), (0,1, 1), (1, -3, A)} is linearly independent, then (A) A = -4 %3D (B) A + 4…

A:

Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: Evaulate ∫C▒1/sinzdz , Where C is the rectangle with vertices at -1-i, 8-i,8+i and -1+i oriented…

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Q: Define the term Change of basis?

A:

Q: Find an algebraic description of the range of A by row reducing A^T and using the relation between…

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Q: Given the vector (x <- c(5, 2, 7), what would x^2 return? O [1] 78 O [1] 196 O [1] 25 4 49 O [1] 10…

A: Given that, the vector is        ,we need to find .

Q: 1 2 3 1[1 1 07 M = 20 0 1 3|1 0 0

A: Write the relation M as a set of ordered pairs. If x,y is an ordered pair in M , then (y,x) is and…

Q: Find a basis for the solution space  x1+3x2+4x3=0 3x1+8x2+7x3=0

A:

Q: One of the following vectors lies in span{ 2+x + æ2, 3+-2a2} (A) 5 + 3x + 4x2 (B) 5 + 3x + 5æ? (C) 5…

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Q: - (0·0-0-0) Is B: - a basis for R³? Explain how you know.

A:

Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

A:

Q: Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain…

A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: Find a basis of Span((1,-1,3,0), (2, 1, -2, -1), (3, 3, -7,-2)).

A: We have to find a basis of Span ((1,-1,3, 0), (2, 1, -2, -1), (3, 3, -7,-2)).

Q: Consider an inner product on two P3 vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2):…

A: Since you have posted multiple subpart question, we will solve the first three sub parts for you. If…

Q: 3) Let C be a basis that contains vectors (−2 + 1x + 1x2 + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 +…

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Q: if the chractrestic polynomial of a matrix A is p(^) = (^ +1)(^ - 2)2 then det(-A) +tr (A) = 1 7 -2…

A: As we have 3 roots of characteristics polynomial.

Q: 1 1 11

A:

Q: Is the set swer. {(1,2,-1,3), (1,-1, 2, 0), (-2, 0, 6, 6)} a basis for R¹? Justify your an-

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Q: Find the vector sum (2, 6) + 3(1, -2) and illustrate with a diagram.

A: Given:2, 6+31, -2