Answer:
a. a(b)c
b. a(a(b)c)c
d. a(a(a(a)c)c)c
Step-by-step explanation:
We are given the following in the question:
a. a(b)c
It is given b belongs to W.
b. a(a(b)c)c
c. a(abc)c
a(abc)c does not belong to W because we cannot find x in W such that a(abc)c belongs to W.
d. a(a(a(a)c)c)c
e. a(aacc)c
a(aacc)c does not belong to W because we cannot find x in W such that a(aacc)c belongs to W.
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.
If the probability of spinning an A once is 1/12, then the probability of spinning an A 3 times is 3 × 1/12.
3 × 1/12 = 3/36
Simplify
3/36 = 1/12
Answer:
m∠QPR = 25°.
Step-by-step explanation:
If m∠QPR = 9x + 16°, substitute in 1 for 'x':. 9(1) + 16 = 9 + 16 = 25°
Hello!
To find the area of a trapezoid you use the equation
Put in the values you know
Add
Divide
Divide both sides by 26
15 = h
The answer is 15km
Hope this helps!
