Final answer:
To find A+B and A-B, add or subtract the corresponding elements of the matrices. For kA, multiply each element of matrix A by the scalar k. These operations require the matrices to have the same dimensions.
Step-by-step explanation:
When A and B are matrices with the same dimension, and k is a real number, the operations are performed element-wise. To find the sum A+B, you simply add the corresponding elements from each matrix. For the difference A-B, subtract the corresponding elements of B from A. Lastly, to find kA, which is a scalar multiplication, multiply each element of matrix A by the scalar k.
Examples:
- If A = [1,2; 3,4] and B = [5,6; 7,8], then A+B = [1+5, 2+6; 3+7, 4+8] = [6,8; 10,12].
- For A-B, it will be [1-5, 2-6; 3-7, 4-8] = [-4,-4; -4,-4].
- If k=3, then kA will be [3×1, 3×2; 3×3, 3×4] = [3,6; 9,12].
The process of adding and subtracting matrices is straightforward, as long as the matrices are of the same size. Scalar multiplication involves multiplying each element of the matrix by the scalar value.