Ch. 6 - Matrices and Determinants

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

Problem 28

Chapter 7, Problem 28

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

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Rewrite the matrix equation 3X + A = B to isolate 3X. Subtract matrix A from both sides: 3X = B - A.

Understand that matrix subtraction (B - A) involves subtracting corresponding elements of matrices B and A. Ensure that matrices B and A have the same dimensions for this operation to be valid.

Once you have the result of B - A, divide each element of the resulting matrix by 3 to solve for X. This is equivalent to multiplying the matrix by the scalar 1/3.

Verify your solution by substituting X back into the original equation 3X + A = B to ensure both sides are equal.

Remember that matrix operations are only valid if the dimensions of the matrices involved are compatible. Double-check the dimensions of A, B, and X to ensure consistency throughout the process.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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, the scalar 3 multiplies every element of matrix X. This concept is essential for simplifying the equation and solving for X, as it directly affects the values within the matrix.

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 the scalar 3, which is necessary to find the value of X.

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