Ch. 6 - Matrices and Determinants

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 6 - Matrices and Determinants

Problema 15d

Capitolo 7, Problema 15d

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Guida verificata passo dopo passo

Step 1: Understand the problem. You are asked to find the matrix expression $-3A + 2B$, where $A$ and $B$ are given matrices.

Step 2: Multiply matrix $A$ by the scalar $-3$. This means multiplying every element of matrix $A$ by $-3$. For example, the element in the first row and first column of $A$ is 2, so after multiplication it becomes $-3 \times 2 = -6$. Do this for all elements of $A$.

Step 3: Multiply matrix $B$ by the scalar $2$. This means multiplying every element of matrix $B$ by $2$. For example, the element in the first row and first column of $B$ is 6, so after multiplication it becomes $2 \times 6 = 12$. Do this for all elements of $B$.

Step 4: Add the resulting matrices from Step 2 and Step 3. To add two matrices, add their corresponding elements. For example, add the element in the first row and first column of the scaled $A$ matrix to the element in the first row and first column of the scaled $B$ matrix.

Step 5: Write the resulting matrix from Step 4 as your final answer for $-3A + 2B$.

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Matrix Addition and Scalar Multiplication

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Scalar multiplication means multiplying every element of a matrix by a constant. These operations are fundamental for combining matrices as in the expression -3A + 2B.

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Matrix Dimensions and Compatibility

For matrix addition or subtraction, the matrices must have the same dimensions (same number of rows and columns). Here, both A and B are 3x3 matrices, so operations like -3A + 2B are valid and can be performed element-wise.

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Introduction to Matrices

Order of Operations in Matrix Expressions

When evaluating expressions like -3A + 2B, scalar multiplication is performed first on each matrix, followed by matrix addition. This ensures the correct combination of matrices and accurate results.

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