1. Find 5A-3B.
A=[6 -5 8], B=[7 5 -6]
[5 -4 3] [4 3 -4]
2. Solve the matrix equation.
[3 -1] - x=[-2 3]
[2 5] [1 -6]
3. Given A=[1 -1 2] and B=[-1 -3 2],
[3 0 5] [2 4 5]
[0 2 -2]
Find AB.
4. What is the inverse of [-100 -25]?
[-5 -6]
wolframalpha can be a great resource here. Enter your matrix as a set of rows. For #1, you'd enter
{{6,-5,8},{5,-4,3}}-{{7,5,-6},{4,3,-4}}
= {{-1,-10,14},{1,-7,7}}
for inverse, just type inverse {...}
Ayo how tf is this still not answered
1. To find 5A-3B, we need to perform scalar multiplication and matrix subtraction.
First, let’s multiply A by 5:
5A = 5 * A = 5 * [6 -5 8; 5 -4 3] = [30 -25 40; 25 -20 15]
Next, let’s multiply B by 3:
3B = 3 * B = 3 * [7 5 -6; 4 3 -4] = [21 15 -18; 12 9 -12]
Now, we subtract 3B from 5A:
5A - 3B = [30 -25 40; 25 -20 15] - [21 15 -18; 12 9 -12] = [30-21 -25-15 40-(-18); 25-12 -20-9 15-(-12)] = [9 -40 58; 13 -29 27]
Therefore, 5A - 3B = [9 -40 58; 13 -29 27].
2. To solve the matrix equation [3 -1] - x = [-2 3], [2 5] [1 -6], we need to isolate the variable x.
We have the equation [3 -1] - x = [-2 3], which can be rearranged as -x = [-2 3] - [3 -1].
= [-2-3 3-(-1)]
= [-5 4].
Now, to solve for x, we multiply both sides of the equation by -1 (to eliminate the negative sign):
-x = [-5 4]
Multiply both sides by -1:
x = [5 -4]
Therefore, x = [5 -4].
3. To find AB, we need to perform matrix multiplication.
Given A = [1 -1 2; 3 0 5] and B = [-1 -3 2; 2 4 5; 0 2 -2], we perform the multiplication as follows:
AB = A * B = [1 -1 2; 3 0 5] * [-1 -3 2; 2 4 5; 0 2 -2]
To calculate the first element of AB, take the dot product of the first row of A with the first column of B:
AB(1,1) = (1*-1) + (-1*2) + (2*0) = -1 - 2 + 0 = -3
Continue this process for the other elements:
AB(1,2) = (1*-3) + (-1*4) + (2*2) = -3 - 4 + 4 = -3
AB(1,3) = (1*2) + (-1*5) + (2*-2) = 2 - 5 - 4 = -7
AB(2,1) = (3*-1) + (0*2) + (5*0) = -3 + 0 + 0 = -3
AB(2,2) = (3*-3) + (0*4) + (5*2) = -9 + 0 + 10 = 1
AB(2,3) = (3*2) + (0*5) + (5*-2) = 6 + 0 - 10 = -4
So, putting it all together, we get:
AB = [-3 -3 -7; -3 1 -4]
Therefore, AB = [-3 -3 -7; -3 1 -4].
4. To find the inverse of a matrix, we can use the formula:
Inverse(A) = (1/det(A)) * adj(A)
Given the matrix A = [-100 -25; -5 -6], we need to find its determinant (det(A)) and adjugate (adj(A)).
To find the determinant, we use the formula:
det(A) = (-100 * -6) - (-25 * -5) = 600 - 125 = 475
Next, to find the adjugate, we need to interchange the elements of the main diagonal and change the sign of the elements in the other diagonal. So, the adjugate of A is:
adj(A) = [-6 -25; -5 -100]
Finally, we can calculate the inverse using the formula:
Inverse(A) = (1/475) * [-6 -25; -5 -100]
Multiplying each element of the adj(A) matrix by 1/475, we get:
Inverse(A) = [6/475 25/475; 5/475 100/475]
Simplifying the fractions, we have:
Inverse(A) = [6/475 1/19; 1/95 20/95]
So, the inverse of the matrix [-100 -25; -5 -6] is [6/475 1/19; 1/95 20/95].