If A=[{:(,1),(,2),(,3):}]and B =[{:(,-5,...

If `A=[{:(,1),(,2),(,3):}]and B =[{:(,-5,4,0),(,0,2,-1),(,1,-3,2):}]"then AB"`

A

`AB=[{:(,-5,8,0),(,0,4,-2),(,3,-9,6):}]`

B

`AB=[-2,-1,4)`

C

`AB=[{:(,-1),(,1),(,1)]`

D

AB does not exist

Text Solution

AI Generated Solution

The correct Answer is:

To solve the problem of multiplying matrices A and B, we first need to define the matrices clearly: Given: - Matrix A = \(\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}\) (which is a 3x1 matrix) - Matrix B = \(\begin{bmatrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \end{bmatrix}\) (which is a 3x3 matrix) ### Step 1: Check the dimensions of the matrices Matrix A has dimensions 3x1 (3 rows and 1 column) and Matrix B has dimensions 3x3 (3 rows and 3 columns). ### Step 2: Determine if multiplication is possible To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. - Matrix A has 1 column. - Matrix B has 3 rows. Since the number of columns in Matrix A (1) is not equal to the number of rows in Matrix B (3), the multiplication \(AB\) is not possible. ### Conclusion Since the multiplication of matrices A and B cannot be performed due to incompatible dimensions, we conclude that \(AB\) does not exist. ### Final Answer The correct option is that \(AB\) does not exist. ---

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