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Calculus Assignment Cross Product

   

Added on  2020-04-29

3 Pages669 Words40 Views
Question 11.False (When we form a matrix from the vectors the determinant is 0, a set of vectors is linearly independent only if the determinant is non-zero.) 2.True (the magnitude of two added vectors can be found by adding the magnitude of the individual vectors.)3.True (the area of the parallelogram is the magnitude of u*v)4.True (vector space {0}=0-dimension)5. True (If A · · → A 0 then Null(A) = Null(A’ ). Elementary row operations were originallydesigned to preserve solutions of equations, so Ax = 0 if and only if A’x = 0.)6False (The rank of a matrix is also equal to the dimension of thecolumn space)Question 21.B (P1 (2,1,-3), P2 (2,6,4), V = P1P2=(2-2, 6-1, 4+3) = (0,5,7))2.C (v1-v2, v1+v2)(2v2,2v1) = (2v1-2v2, 2v1+2v2)3.A (kv = k(2, 1, -2) = (2k, k, -2k). magnitude kv = 9k2=122; k=4)4.C (The rank of anm×nmatrix is anonnegativeintegerand cannot be greater than eithermorn)5.A (rank A+ nullity A = n; where n=number of columns. Nullity = (8-3) = 5 )6.C (two vectorsareorthogonalif and only if their dot product is zero. (1,2, 0,−1).(-2,3,1,4)=0)Question 3The cross-product of two vectors is found by;[ijkabcdef] = (bf-ce)i – (af-cd)j + (ae-bd)kSubstituting;[ijk111−263] = (3-6)i – (3+2)j + (6+2)k= -3i-5j+8k= 0Question 4Span W(a, b ∈R)a + b ∈ WThe zero vector is in W because we take k=0

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