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Linear Algebra
Let T : R3 -> R3 be the linear operator
defined by T(x1, x2, x3) = (x1, x3, -2x2 - x3).
Let f(x) = - x³ + 2. Find the operator f(T).
defined by T(x1, x2, x3) = (x1, x3, -2x2 - x3).
Let f(x) = - x³ + 2. Find the operator f(T).
Linear Algebra
Suppose a1 = (1, 0, 1), a2 = (0, 1, -2) and
a3 = (-1, -1, 0) are vectors in R³ and
f : R³ -> R is a linear functional such that
f(a1) = 1, f(a2) = -1 and f(a3) = 3. If
a = (p,q,r) belongs to R3, find f(a).
a3 = (-1, -1, 0) are vectors in R³ and
f : R³ -> R is a linear functional such that
f(a1) = 1, f(a2) = -1 and f(a3) = 3. If
a = (p,q,r) belongs to R3, find f(a).
Linear Algebra
Let B = f(a1,a2, a3) be an ordered basis of
R³ with a1 = (1, 0, -1), a2 = (1, 1, 1),
a3 = (1, 0, 0). Write the vector v = (a, b, c) as
a linear combination of the basis vectors
from B.
R³ with a1 = (1, 0, -1), a2 = (1, 1, 1),
a3 = (1, 0, 0). Write the vector v = (a, b, c) as
a linear combination of the basis vectors
from B.
Linear Algebra
company produces three products P, Q and R using raw materials A, B and C. One unit of P requires 1, 2 and 3 units of A, B and C respectively. One unit of Q requires 2, 3 and 2 units of A, B and C respectively. One unit of R requires 1, 2 and 2 units of A, B and C respectively. The number of units available for raw material A, B and C are 8, 14 and 13 units respectively. Using the matrix method, determine the number of units of each product to produce in order to utilize completely the available resources. (6 Marks)
Linear Algebra
Show whether the first three vectors are linearly independent
V1= 1, 1, 2, -2
V2= 2, -3, 0, 2
V3= -2, 0, 2, 2
V4= 3, -3 -2, 2
V1= 1, 1, 2, -2
V2= 2, -3, 0, 2
V3= -2, 0, 2, 2
V4= 3, -3 -2, 2
Linear Algebra
A company produces three products P, Q and R using raw materials A, B and C. One unit of P requires 1, 2 and 3 units of A, B and C respectively. One unit of Q requires 2, 3 and 2 units of A, B and C respectively. One unit of R requires 1, 2 and 2 units of A, B and C respectively. The number of units available for raw material A, B and C are 8, 14 and 13 units respectively. Using the matrix method, determine the number of units of each product to produce in order to utilize completely the available resources.
Linear Algebra
Orthogonal
Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w. Why so?
Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w. Why so?
Linear Algebra
Dot Product
Suppose that u and v are vectors in R to the seventh power both of length 2 the square root of 2 and that the length of u − v is also2 the square root of 2 . Then parallel to u plus v parallel-to = ____________ and the angle between u and v is _____________.
Suppose that u and v are vectors in R to the seventh power both of length 2 the square root of 2 and that the length of u − v is also2 the square root of 2 . Then parallel to u plus v parallel-to = ____________ and the angle between u and v is _____________.
Linear Algebra
Let v be a vector space over F, define a spanning of v.
Linear Algebra
Write the vector v=( 1, -2, 5) as a linear combination of the vector e1=( 1, 1, 1), e2= ( 1, 2, 3) and e3=( 2, -1, 1)
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#339914 on Dec 2023
#339914 on Dec 2023