Given v = U₁ = 0 find the coordinates for v in the subspace W spanned by 1 [3] 0 -1 V = -9 3.33 -3 7 3 5 1 4 Note that u₁, 2, 3 and 4 are orthogonal. 1 , U₂ = , uz = U1 + -0.275 11 [3] -1 4 -7 and u4= u2+ -0.776 [3] -3 1 1 u3+ 2.818 us

Q: give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a.…

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Q: 1 -3 0 Let v¹ 3 1 ,w= -5 and determine if w is in the subspace of R³ -2 2 generated by v¹ and v².…

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Q: Find a basis for the indicated subspace of R³. The line of intersection of the planes with equations…

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

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Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

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A: The vectors u1, u2, u3, u4, u5 are orthogonal. Therefore, ui·uj=0, for i≠j. Consider the given…

Q: The vector x is in a subspace H with a basis B = {b₁,b₂). Find the B-coordinate vector of x. 2 b₁ =…

A: We are given that           b1 = (2, -3)t          b2 = (-1, 5)t        Now, x is in H with the…

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Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

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Q: Given v = find the coordinates for v in the subspace W spanned by -7 u1 = and uz -1 -28 Note that uj…

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Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

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A: Given v1 = 10-2v2 = 311v3 = 612w = 321 The equation x1v1+x2v2+x3v3=w will have a solution if the…

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Q: Let W be the subspace spanned by u₁ and u2, and write y as the sum of a vector in W and a vector…

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Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

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A: Given: y=-8-1-5-10, u1=-56-61, u2=0-4-7-18To find: The distance, d from y to the subspace of ℝ4.

Q: -8 Given v = -7 find the coordinates for v in the subspace W spanned by -1 4 -3 u1 3 , U2 and U3 -17…

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