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Are the following matrices invertible ? ...

Are the following matrices invertible ?
`|{:(2,-3),(1,4):}|`
(ii) `|{:(7,0),(3,1):}|`
(iii) `|{:(1,-2,-3),(1,-3,-4),(1,-4,-5):}|`
(iv) `|{:(2,3,-1),(0,1,4),(-5,0,-2):}|`
(v) `|{:(0,1,2),(1,2,3),(3,1,1):}|`

Text Solution

Verified by Experts

The correct Answer is:
(i),(ii),(iv) are invertible
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Find the inverse of the following matrices if exist : (i) |{:(5,-3),(2,2):}| (ii) |{:(1,-3),(-1,2):}| (iii) |{:(1,0,-1),(3,4,5),(0,-6,-7):}| (iv) |{:(1,-3,3),(2,2,-4),(2,0,2):}| (v) |{:(1,2,1),(1,-1,-2),(1,2,-1):}| (vi) |{:(4,-2,-1),(1,1,-1),(-1,2,4):}|

Evalute the determinants : (i) |{:(3,-1,-2),(0,0,1),(3,-5,0):}| (ii) |{:(3,-4,5),(1,1,-2),(2,3,1):}| (iii) |{:(0,1,2),(-1,0,-3),(-2,3,0):}| (iv) |{:(2,-1,-2),(0,2,-1),(3,-5,0):}|

Knowledge Check

  • If A{:[(7,6,-1),(4,2,3),(1,3,0)]:}={:[(4,2,3),(1,2,0),(7,6,-1)]:} then A=

    A
    `{:[(1,0,0),(0,0,1),(0,1,0)]:}`
    B
    `{:[(1,0,0),(0,1,0),(0,0,1)]:}`
    C
    `{:[(0,1,0),(1,0,0),(0,0,1)]:}`
    D
    `{:[(0,1,0),(0,0,1),(1,0,0)]:}`

  • If {:A*[(7,6,-1),(4,2,3),(1,3,0)]:}={:[(4,2,3),(1,3,0),(7,6,-1)]:} , then A =

    A
    `{:[(1,0,0),(0,1,0),(0,0,1)]:}`
    B
    `{:[(1,0,0),(0,0,1),(0,0,1)]:}`
    C
    `{:[(0,1,0),(0,0,1),(1,0,0)]:}`
    D
    `{:[(0,1,0),(0,0,1),(0,0,1)]:}`

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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):}]

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