If A= [2−185−32]%0D%0A[%0D%0A2%0D%0A8%0D%0A−%0D%0A3%0D%0A−%0D%0A1%0D%0A5%0D%0A2%0D%0A]%0D%0A and B= [−10035−2]%0D%0A[%0D%0A−%0D%0A1%0D%0A0%0D%0A5%0D%0A0%0D%0A3%0D%0A−%0D%0A2%0D%0A]%0D%0A , what is 4A+3B? Solve algebraically, showing all steps.
To find the expression 4A + 3B, we need to multiply each element in matrix A by 4 and each element in matrix B by 3, and then add the corresponding elements together.
First, let's find 4A:
4A = 4 * [2 -1 8 -3 -1] = [8 -4 32 -12 -4]
[5 2 10 -6 2]
Next, let's find 3B:
3B = 3 * [-10 3 -2] = [-30 9 -6]
[0 15 9]
[-2 -6 -3]
Now, let's add the corresponding elements together:
4A + 3B = [8 -4 32 -12 -4] + [-30 9 -6] = [-22 5 26 -12 -4]
[5 2 10 -6 2] [0 15 9] [5 17 9]
[-2 -6 -3]
Therefore, 4A + 3B is equal to:
[-22 5 26 -12 -4]
[5 17 9]
[-2 -6 -3]
To solve the equation 4A + 3B, we need to perform scalar multiplication on both matrices A and B, and then add the resulting matrices together.
Given A = [2 -1 8; -3 2 -1; 5 2] and B = [-10 35 -2; -1 0 5; 0 3 -2], we will first perform scalar multiplication.
Step 1: Scalar multiplication of A
Multiply each element of matrix A by 4:
4A = [4*2 4*(-1) 4*8; 4*(-3) 4*2 4*(-1); 4*5 4*2]
Simplifying, we have:
4A = [8 -4 32; -12 8 -4; 20 8]
Step 2: Scalar multiplication of B
Multiply each element of matrix B by 3:
3B = [3*(-10) 3*35 3*(-2); 3*(-1) 3*0 3*5; 3*0 3*3 3*(-2)]
Simplifying, we have:
3B = [-30 105 -6; -3 0 15; 0 9 -6]
Step 3: Matrix addition
Add the corresponding elements of 4A and 3B:
4A + 3B = [8-30 -4+105 32-6; -12-3 8+0 -4+15; 20+0 8+9]
Simplifying, we have:
4A + 3B = [-22 101 26; -15 8 11; 20 17]
Therefore, the solution to 4A + 3B is:
4A + 3B = [-22 101 26; -15 8 11; 20 17]
To find the value of 4A + 3B, we need to multiply each element of matrix A by 4, and each element of matrix B by 3, and then add the corresponding elements together.
Given that:
A = [2 -1 8
-3 2 -1
5 2]
B = [-10 3 -2
-1 0 5
0 3 -2]
We can proceed with the calculations step by step.
First, let's multiply each element of matrix A by 4:
4A = [4*2 4*(-1) 4*8
4*(-3) 4*2 4*(-1)
4*5 4*2]
= [8 -4 32
-12 8 -4
20 8]
Next, multiply each element of matrix B by 3:
3B = [3*(-10) 3*3 3*(-2)
3*(-1) 3*0 3*5
3*0 3*3 3*(-2)]
= [-30 9 -6
-3 0 15
0 9 -6]
Finally, we add the corresponding elements of 4A and 3B:
4A + 3B = [8 -4 32 + -30 9 -6
-12 8 -4 + -3 0 15
20 8 + 0 9 -6]
= [-22 5 26
-15 8 11
20 17 -6]
Therefore, 4A + 3B is equal to the matrix:
[-22 5 26
-15 8 11
20 17 -6]