Suppose T: R³-R² is a linear transformation. Let u, v and w be the vectors given below, and suppose that T(u) and T(v) are as given. Find T(w). 1 9 ---B u= 2 V = 5 W = -9 T(u) -3 0 T(w) = 0 0 -3 8 -[3] = T(v)

Q: [1 2] 3 6 Let A = Write the vector u = (4,3) as u = u, + u„ where u̟ and un belong to the row space…

A: The given matrix is A=1236. Obtain the reduced row echelon form of matrix A as follows…

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

A:

Q: Are the vectors u = (-3,0,2), v = (-2,-3,0), and v= (-16, -15, 4) linearly dependent? if yes, find a…

A:

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: Which of the following sets of vectors in R° are linearly dependent? Note. Mark all your choices. O…

A: We say a set of vectors v1, v2, ...., vn is linearly independent if…

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

A:

Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: 18 as a linear combination of a and y Express the vector v y.

A:

Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

Q: Determine the values(s) of h, if any, for the which the set of vectors {a1.a2,a3} is a linearly…

A:

Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: 4. Prove that the vector given by (2xy -y')7+(2x²y-3xy² +2) 7 is a gradient. Also, find the function…

A: The solution are next step

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

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

A:

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

A:

Q: Which of the following is a direction vector for the line through А (3, — 2) and В (1, 2)? Select…

A:

Q: Let j TE 2 --- = 1 and u = = Write y as the sum of two orthogonal vectors, #₁ in Span{u} and 2…

A:

Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

A:

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: 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: In each part, determine whether the vectors are linearly inde- pendent or are linearly dependent in…

A: