Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and 7 in R³ such that W = span{ū, v}.

Q: Q12: Let vector v = (1, 3) and vector w=(-4,-2). Write vector v as the sum of two orthogonal…

A:

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V1, V2, V3) such…

A:

Q: Q11: Let vector v = (-7, 5) and vector w=(2, 2). Write vector v as the sum of two orthogonal…

A:

Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

A:

Q: Let l be a straight line that passes through the origin and is parallel to the vectors…

A:

Q: Determine whether the vectors v₁ = (1, 2), v₂ = (-1,0) and v3 = (0, 1) are linearly independent; if…

A:

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

A:

Q: |3s + 3t Let W be the set of all vectors of the form 3s - 4t. Find vectors u and v in R³ such that…

A:

Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

A:

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

A:

Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

A:

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

Q: Find all vectors (x,y,z) that are orthogonal to the vectors (1,2,3) and (4,5,6). Find the vector in…

A: