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.
Answer:
-3>=x this is because the circle is closed as well as the arrow going the opposite from -3
Step-by-step explanation:
Answer:
I dont know
Step-by-step explanation:
how to answer that
2.5 still if you make it a fraction it would be 2 and 1 1/2 so you can't simplify that any more
Answer:
Step-by-step explanation:
A salt solution contains 10% salt and weights 80g.
<u>Salt content of the solution is:</u>
<u>4% solution has 8 g salt, total solution is:</u>
- 0.04x = 8
- x = 8/0.04 = 200 g
<u>Water to be added:</u>