Determine if the following statement is true or false:If {v1,v2,v3} is an orthogonal basis for  a subspace W, then the set {a⋅v1,b⋅v2,c⋅v3}(where a,b,c are nonzero scalars) is an orthogonal basis for W.TrueFalse

A set of three vectors {v1,v2,v3}{𝑣1,𝑣2,𝑣3}   in a vector space is an orthogonal set if each is vector is a non-zero vector, and if every vector is orthogonal with the other two. This means explicitly thatv1⋅v2=v2⋅v3=v3⋅v1=0.𝑣1⋅𝑣2=𝑣2⋅𝑣3=𝑣3⋅𝑣1=0.   So for example ⎧⎩⎨⎪⎪⎛⎝⎜341⎞⎠⎟,⎛⎝⎜5−2−7⎞⎠⎟,⎛⎝⎜1−11⎞⎠⎟⎫⎭⎬⎪⎪{(341),(5−2−7),(1−11)}   is an orthogonal set in R3𝑅3   . Can you find a set of three orthogonal vectors in R3𝑅3   which includes the vector ⎛⎝⎜4−12⎞⎠⎟?(4−12)?     Such a set is

Let be U = Span{[3,0,1]} a subspace of W=Span{[1,0,0],[1,0,1]}, and the space V the orthogonal complement of U. Answer these two following questions:1. Give a basis v=[ , , ] for V,2. Give dim V = .(If your result is not an integer, then please give your result with 2 decimals (rounded - not cut-off; use a dot as a decimal separator))

YouLet v1=[-1 4 0 0 0 -1], v2=[-5 0 2 -1 0 -2], v3=[5 0 0 3 3 5]Use the Gram-Schmidt procedure to produce an orthogonal set with the same span. what is u1, <u1, v2>, <u1, u1>, u2, <u1, v3>, <u2, v3>, <u2, u2>, and u3.

Let U be the subspace spanned by the orthogonal set {[1, 2, 3],[-1, -1,1]} and x=[0, 2, 1]. Let v = (a, b, c) be the projection of x on U. Find a.Select one:a. 5/6b. -2/3c. 5/3d. -7/6e. None of the other choices is correct

Let x=[1, 0, -1], and let U be the subspace spanned by the orthogonal set {[2, 1, -1],[1,1,3]}. Vector x can be written as x=x1+x2, where x1 is in U and x2 is orthogonal to U. Find the first coordinate of x2.Select one:a. 4/11b. 6/11c. None of the other choices is correctd. 5/11e. 3/11