#7 A triangle has vertices A,B,C as shown in the diagram. It has been translated vertically and/or horizontally to the triangle with vertices labelled A, B, and  C using a translation matrix defined as .

Q: iv) Find a basis for ker(T). 1o lamsd zied v) Determine the dimension of the ker(T). vi) Find a…

A: Given Transformation convert to the matrix T(w)= 3-6  2-2 4  1 1-2-1-1 2  2 Transform the matrix to…

Q: 3. Do the following sets of vectors in R3 have the same span? and w₁ = (1, -2,-5), w2 = (0,8,9) vi=…

A: The span of a set of vectors, also called linear span, is the linear space formed by all the vectors…

Q: 1. For the 3-node triangular graph in the figure following, write the 3 by 3 incidence matrix A.…

A: Given data:-

Q: B) Let B=38 3 O 6 1 1 50 Compute det (B-¹).

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Q: (Section 5.3) i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and v3 = (1,3,3,3)…

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Q: Let B To which point do the linear maps associated with A and B map the points (1, – 9) and (4, 4)?…

A: we know  Tx=Ax Given,  A=1038B=-40-12

Q: d 3. Find the herrel of the linear transformati L: R³ R³ with matrix 2 5 1 390 1 4 -1

A: To find kernel, we have to find null space of corresponding matrix.

Q: 3. Let A be the vector (6, 7, 0, 9, 15), B be the vector (a, b, c, d, e), and C be the vector (-4,…

A: Answer:- Given, the vectors A  = (6, 7, 0, 9, 15), B = (a, b, c, d, e) and  C = (-4, -1, -2, 0, -15)…

Q: b) Then find the projection of b=(3,1,-3,4) onto the column space of 0 1 A 1 1 1 2

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Q: 1.6 Find the vector projection, ProjgA and ProjĄB When A = i+ 2j + k and B = k.

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Q: Do NOT row reduce! (a) Write the augmented matrix whose row reduction would find [x]B . (b) Write…

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Q: 2. Determine if the following vectors constitute a linearly independent set.

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Q: 4. Let T be a rotation by 90° (clockwise), as a linear transformation from R2 to R2. Let S be a…

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Q: Q1. Consider the 3D shape with the following vertices: 4-38-60-60-98-88-8 A=5,B=5,C = 5,D = 5,E =…

A: Step 1: Step 2: Step 3: Step 4:

Q: 10. a = -2i+ j – 3k, b = 2j – k %3D

A: Given:- a = - 2i + j - 3k, b = 2j - k To find:- aXb

Q: Consider the relation R = {(a, 6), (6, 6), (6, c), (c, b), (c, c), (d, a), (d, c), (d, d)} on {a, 6,…

A: Given: R=a,b,b,b,b,c,c,b,c,c,d,a,d,c,d,d (a) Diagraph of R is as follows: