Verify that {u₁.₂) is an orthogonal set, and then find the orthogonal projection of y onto Span {₁,₂}- y = 6 5,4₁ -3 0 4₂ To verify that {u₁.4₂} is an orthogonal set, find u₁ • U₂- U₁ • U₂ = (Simplify your answer.)

Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 2. Describe a linear map which maps the set of vectors (-²2) 0 (6) (2) to the set of vectors

A: Introduction:  As per the guidelines i solves first question. For more solutions please repost the…

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

A:

Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: (b) Let v₁ = (-2, 1,5), v₂ = (0, 1,4), V3 = (-2,4, 17). What is span(V1, V2, V3)? Could it be all of…

A: Given vectors are v1=(-2,2,5), v2=(0,1,4),v3=(-2,4,17) we have to find span(v1,v2,v3)

Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

A:

Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4v, - v,, 4v, +…

A:

Q: b) Let l and l2 be lines in 3 space such that 2. 4 passes through the point with coordinates (3, 4,…

A:

Q: Prove that three points P(5,-4), Q(-3,8) and R(1,2) on the rectangular coordinate plane are…

A:

Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

A:

Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

A:

Q: Suppose that v1 = (5, 2, 0, 3), v2 = (2, -2, 8, 2) and v3 = (-6, 0, 5, 4). Is the following vector…

A:

Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

A:

Q: Suppose that v1 = (5, 1, 0, 5), v2 = (5, -3, 6, 2) and v3 = (-5,0, 5, 2). %3! Is the following…

A:

Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

A:

Q: Use the function to find the image of v and the preimage of w. T(V, V2, V3) = (4v, - V, 4v, + 5v2),…

A:

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, +…

A:

Q: Suppose that a parallelogram is bounded at one vertex by the vectors i = |,3 = ,: Find the area of…

A: Area of parallelogram =|u×v| ,where u and v are the vectors which represent the side of…

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

A:

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: and .We have to find .

Q: Determine the new coordinates of the point (3,5) when the origin is moved to (2,4) by translation…

A: We have to find the point

Q: A crossed belt connects a 16-centimeter pulley (x = 8-cm radius) on an electric motor with a…

A: Given information:The radius of pulley on saw and motor is 16 cm and 8 cm respectively, which…

Q: lowing vector in the span{V₁, V₂, V3}? 8,9) me vector is in the span. me vector is not in the span.

A:

Q: Suppose that v1 = (4, 1, 0, 4), v2 = (2, -4, 5, 2) and v3 = (-2, 0, 3, 6). Is the following vector…

A: