Perform the operation for each equation, if there is a solution (Matrices)
[4k -8y ] [5k+6y 2k+1]
[6z - 3x] - [2z+5x z+4]
[2k + 5a] [4k+6a 3a+2]
To perform operations on matrices, we need to follow certain rules.
For addition and subtraction of matrices, we simply add or subtract corresponding elements of the matrices.
For example, to perform the operation [4k -8y] + [5k+6y 2k+1]:
- Add the corresponding elements of the matrices:
- (4k + 5k) = 9k
- (-8y + 6y) = -2y
So, the resulting matrix would be [9k -2y 2k+1].
To perform the operation [6z - 3x] - [2z+5x z+4]:
- Subtract the corresponding elements of the matrices:
- (6z - 2z) = 4z
- (-3x - 5x) = -8x
So, the resulting matrix would be [4z -8x z+4].
To perform the operation [2k + 5a] multiplied by [4k+6a 3a+2]:
- Multiply each element from the first matrix by the corresponding element in the second matrix and add the results.
- (2k * 4k) + (5a * 3a) = 8k^2 + 15a^2
- (2k * 6a) + (5a * 2) = 12ak + 10a
- (2k * 4k) + (5a * 3a) = 8k^2 + 15a^2
- (2k * 6a) + (5a * 2) = 12ak + 10a
So, the resulting matrix would be [8k^2 + 12ak + 15a^2 12ak + 10a].