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:
7 hours and 20 minutes.
Step-by-step explanation:
Firstly, to calculate a price you need to change the percentage into a decimal. You do this by dividing it by 100.
30 / 100 = 0.3
The price will be 70% of the original price,
70 / 100 = 0.7,
0.7 * 53 = 37.10,
The sale price of the sweater will be $37.10.
Hope this helps!
Step-by-step explanation:
I tried. if I got this wrong I might need to go back to kindergarten
Given:
Morning Temperature = 15 degrees, Afternoon Temperature = 30 degrees
Morning Temperature = 20 degrees, Afternoon Temperature = 40 degrees
Morning Temperature = 26 degrees, Afternoon Temperature = 52 degrees
To find:
The ratio of the afternoon to morning.
Solution:
Taking any one pair of morning and afternoon temperature, we can find the ratio.
Morning Temperature = 15 degrees
Afternoon Temperature = 30 degrees
Therefore, the correct option is C.