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Compute AB and BA, whichever exists when...

Compute AB and BA, whichever exists when
(i) `A=[{:(2,-1),(3," "0),(-1," "4):}]" and "B=[{:(-2,3),(0,4):}]`
(ii) `A=[{:(-1,1),(-2,2),(-3,3):}]" and "B=[{:(" "3,-2," "1),(" "0," "1," "2),(-3," "4,-5):}]`
(iii) `A=[{:(0,1,-5),(2,4," "0):}]" and "B=[{:(1,3),(-1,0),(0,5):}]`
(iv) `A=[1" "2" "3" "4]" and "B=[{:(1),(2),(3),(4):}]`
(v) `A=[{:(2,1),(3,2),(-1,1):}]" and "B=[{:(1,0,1),(-1,2,1):}]`

Text Solution

AI Generated Solution

To compute the products \(AB\) and \(BA\) for the given matrices, we will follow the steps outlined below for each part of the question. ### (i) Given: \[ A = \begin{pmatrix} 2 & -1 \\ 3 & 0 \\ -1 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} -2 & 3 \\ 0 & 4 \end{pmatrix} \] **Step 1: Determine the dimensions of matrices A and B.** - Matrix \(A\) is \(3 \times 2\) (3 rows and 2 columns). - Matrix \(B\) is \(2 \times 2\) (2 rows and 2 columns). ...
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Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]

Given A=[{:(2,4,0),(3,9,6):}] "and" B=[{:(1,4),(2,8),(1,3):}] , is (AB)=B'A'?

Knowledge Check

  • If A=[{:(3,1,2),(1,2,-3):}]" and "B=[{:(-2," "0,4),(5,-3,2):}] , find (2A-B).

    A
    `[{:(8,2," "0),(3,7,-8):}]`
    B
    `[{:(8,2," "0),(-3,7,-8):}]`
    C
    `[{:(8,2," "0),(-3,7," "8):}]`
    D
    `[{:(8,2," "0),(3,7,8):}]`

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

    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

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    Verify that A(B+C)=(AB+AC), when (i) A=[{:(1,2),(3,4):}],B=[{:(2," "0),(1,-3):}]" and "C=[{:(1,-1),(0," "1):}]. (ii) A=[{:(2,3),(-1,4),(0,1):}],B=[{:(5,-3),(2," "1):}]" and "C=[{:(-1,2),(" "3,4):}].

    if A=[{:(4,0,-3),(1,2,0):}]and B=[{:(2,1),(1,-2),(3,4):}]' then find AB and BA.

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