Let 𝐀 :=[ 2 1 0 4 -1 3 ] and 𝐁 :=[ 1 1 -1 0 3 1 ]. Find: (a)

Name: Problem 4, Chapter 9: Fundamentals of Differential Equations
Uploaded: 2019-07-31T12:19:33-08:00
Duration: 6 min 19 s
Channel: Fan Yang
Description: Let 𝐀 :=[ 2 1 0 4 -1 3 ] and 𝐁 :=[ 1 1 -1 0 3 1 ]. Find: (a) AB. (b) BA.

step 1 For question A, we're looking for the products of AB. So first of all, let's write down the matr

Question

Let $$\mathbf{A} :=\left[ \begin{array}{rr}{2} & {1} \\ {0} & {4} \\ {-1} & {3}\end{array}\right]$$ and $$\mathbf{B} :=\left[ \begin{array}{rrr}{1} & {1} & {-1} \\ {0} & {3} & {1}\end{array}\right].$$ Find: (a) AB. $\quad$ (b) BA.

   Let $$\mathbf{A} :=\left[ \begin{array}{rr}{2} & {1} \\ {0} & {4} \\ {-1} & {3}\end{array}\right]$$ and $$\mathbf{B} :=\left[ \begin{array}{rrr}{1} & {1} & {-1} \\ {0} & {3} & {1}\end{array}\right].$$
Find: (a) AB. $\quad$ (b) BA.

Fundamentals of Differential Equations

R. Kent Nagle 9th Edition

Chapter 9, Problem 4

Instant Answer

Solved by Expert Fan Yang

07/31/2019

Step 1

The product of two matrices is calculated by taking the dot product of the rows of the first matrix with the columns of the second matrix. Show more…

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Let $$\mathbf{A} :=\left[ \begin{array}{rr}{2} & {1} \\ {0} & {4} \\ {-1} & {3}\end{array}\right]$$ and $$\mathbf{B} :=\left[ \begin{array}{rrr}{1} & {1} & {-1} \\ {0} & {3} & {1}\end{array}\right].$$ Find: (a) AB. $\quad$ (b) BA.

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Key Concepts

Non-Commutativity of Matrix Multiplication

Matrix multiplication is generally non-commutative; that is, switching the order of multiplication (i.e., computing AB versus BA) can yield different results or may even be undefined if the dimensions are incompatible. This property is central when dealing with products of matrices.

Matrix Multiplication

Matrix multiplication is the process of combining two matrices by taking the dot product of rows from the first matrix with columns from the second matrix. This operation involves summing the products of corresponding elements, and it produces a new matrix with entries defined by these sums.

Dimensional Compatibility

For two matrices to be multiplied, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The dimensions of the resulting matrix are determined by the number of rows in the first matrix and the number of columns in the second matrix.

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