Solve for X in the matrix equation 3X+A = B where

Verified step by step guidance

1. Insert step 1: Understand the problem. We are given a matrix equation 3X + A = B, where X, A, and B are matrices. Our goal is to solve for the matrix X.
2. Insert step 2: Isolate the term with X. To do this, subtract matrix A from both sides of the equation. This gives us 3X = B - A.
3. Insert step 3: Solve for X. Since 3X means 3 times the matrix X, we need to divide both sides of the equation by 3 to solve for X. This can be done by multiplying both sides by the scalar 1/3.
4. Insert step 4: Express the solution. The equation becomes X = (1/3)(B - A), which means you multiply the resulting matrix (B - A) by the scalar 1/3.
5. Insert step 5: Verify the solution. Once you have calculated X, you can substitute it back into the original equation to ensure that 3X + A equals B, confirming the solution is correct.

Key Concepts

Matrix Operations

Matrix operations, including addition, subtraction, and scalar multiplication, are fundamental in linear algebra. In the context of the equation 3X + A = B, understanding how to manipulate matrices is crucial. For instance, you need to know how to add matrix A to the product of 3 and matrix X to isolate X.

Scalar Multiplication

Scalar multiplication involves multiplying each element of a matrix by a scalar (a single number). In the equation 3X + A = B, the term 3X indicates that every element of matrix X is multiplied by 3. This concept is essential for simplifying the equation and solving for X.

Isolating Variables

Isolating variables is a key algebraic technique used to solve equations. In the equation 3X + A = B, the goal is to isolate X. This involves rearranging the equation by subtracting matrix A from both sides and then dividing by 3, which requires an understanding of matrix inverses if applicable.