Find the following matrices: A + B A + B A = [ 2 − 4 1 ] , B = [ − 5 3 − 1 ] A = \begin{bmatrix}2 \\-4 \\1\end{bmatrix}, B = \begin{bmatrix}-5 \\3 \\-1\end{bmatrix} A = 2 − 4 1 , B = − 5 3 − 1

Hey everyone here we are asked to perform the matrix operation A plus B. Now, before we begin solving we want to first substitute in the given matrices to their corresponding variable. So first we have matrix A. Which is given as a three by one matrix with the values five negative six and two. And then we have plus matrix B which is also a three by one matrix. But instead with the values negative +70 and negative three. So now we just have to add each value from A. To the corresponding value from B. So doing this we have five plus negative seven which is the first value from A. And the first value from B. Then we take the second value from a negative six plus the second value from B which is zero. And lastly the third value from A. Which is two plus the third value of B which is negative three. And now we just have to simplify and we find that A plus B is the three by one matrix with the values five plus negative seven giving us negative two negative six plus zero which is just negative six and two plus negative one which gives us negative one. And therefore we are left with answer choice. A Thanks for watching. I hope you found this video helpful and I'll see you again next time

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

1:41 minutes

Problem 13a

Textbook Question

Find the following matrices: $A + B$
$A = \begin{bmatrix}2 \\-4 \\1\end{bmatrix}, B = \begin{bmatrix}-5 \\3 \\-1\end{bmatrix}$

Verified step by step guidance

Identify the given matrices: $ A = \begin{bmatrix} 2 \\ -4 \\ 1 \end{bmatrix} $ and $ B = \begin{bmatrix} -5 \\ 3 \\ -1 \end{bmatrix} $.

Calculate the scalar multiplication of matrix $ B $ by 2: multiply each element of $ B $ by 2 to get $ 2B = \begin{bmatrix} 2 \times (-5) \\ 2 \times 3 \\ 2 \times (-1) \end{bmatrix} $.

Calculate the scalar multiplication of matrix $ A $ by 5: multiply each element of $ A $ by 5 to get $ 5A = \begin{bmatrix} 5 \times 2 \\ 5 \times (-4) \\ 5 \times 1 \end{bmatrix} $.

Calculate the expression $ A + 2B - 5A $ by performing matrix addition and subtraction element-wise: $ A + 2B - 5A = (A - 5A) + 2B = (-4A) + 2B $.

Perform the element-wise operations to combine the matrices: multiply $ A $ by -4, then add the resulting matrix to $ 2B $ to get the final matrix.

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Key Concepts

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

Matrix Addition

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is the sum of elements in the same position from the original matrices. This operation is only defined when both matrices have identical sizes.

Scalar Multiplication of a Matrix

Scalar multiplication means multiplying every element of a matrix by a constant (scalar). This operation scales the matrix by the scalar value, changing the magnitude of each element but not the matrix's dimensions.

Matrix Dimensions and Compatibility

Understanding matrix dimensions is crucial for performing operations like addition and scalar multiplication. Two matrices can be added only if they have the same number of rows and columns. Scalar multiplication can be applied to any matrix regardless of its size.

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