Question

reduce the matrix 1 2 3 0 - 2 4 3 2 - 3 2 1 3 - 6 8 7 5 into normal form and find its rank. its a 4 × 4 matrix​

Answer 1

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Reduce the matrix A to normal form and hence find its rank where ⎡⎣⎢115−1333−336−411⎤⎦⎥

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gravatar for shaily.mishra30 shaily.mishra30 • 190

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rank of the matrix• 11k views

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written 4.6 years ago by

gravatar for shaily.mishra30 shaily.mishra30 • 190

A=⎡⎣⎢115−1333−336−411⎤⎦⎥R2→R2−R1,R3→R3−5R1∴A=⎡⎣⎢100−1483−6−126−10−19⎤⎦⎥C3→C3+C2∴A=⎡⎣⎢100−1482−2−46−10−19⎤⎦⎥R3→R3−2R2∴A=⎡⎣⎢100−1402−206−101⎤⎦⎥R1→R1−6R3,R2→R2−10R3∴A=⎡⎣⎢100−1402−20001⎤⎦⎥R1→R1+R2,C3→C3×2∴A=⎡⎣⎢1003400−40001⎤⎦⎥C2→C2−3C1∴A=⎡⎣⎢1000400−40001⎤⎦⎥C3→C3+C2,C3⟷C4∴A=⎡⎣⎢100040001000⎤⎦⎥R2→R2×14∴A=⎡⎣⎢100010001000⎤⎦⎥HenceRank=3

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Answer 2

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