A is a square matrix of order n.l= maximum number of distinct entries if A is a triangular matrixm= maximum number of distinct entries if A is a diagonal matrixp= minimum number of zeroes if A is a triangular matrixIf l+5=p+2m, find the order of the matrix.

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Filo · Accepted Answer

A is a square matrix of order nL= maximum number of distinct entries if A is triangular.Lets assume all the non-zero elements in the triangular matrix are distinct.So maximum number is =1+2+3+.........+nbecause in the first column there is one non zero elements, in second column there are two elements and in the nth column n elements.So here L=1+2+3+.........+n−2n(n+1)​ m= maximum number of distinct entries if A is diagonal.Lets assume all the non zero elements are distinct. So in each column there is one non-zero element so m=n numbers1+1+1+........+1​​So m=nP= minimum number of zeros in A if A is triangularLets assume all the elements in and above or below of the diagonal in the triangular matrix is non-zero.So minimum number of 0′s=n2−2n(n+1)​P=22n2−n2−n​P=2n2−n​L+5=P+2m2n(n+1)​+5=2n2−n​+2n2n2+n+10​=2n2−n+4n​n2+n+10=n2+3n2n=10n=5 So order of the matrix =5

Question Text	$A$ is a square matrix of order $n$ . $l =$ maximum number of distinct entries if $A$ is a triangular matrix $m =$ maximum number of distinct entries if $A$ is a diagonal matrix $p =$ minimum number of zeroes if $A$ is a triangular matrix If $l + 5 = p + 2 m$ , find the order of the matrix.
Answer Type	Text solution:1
Upvotes	162

$A$ is a square matrix of order $n$ .
$l =$ maximum number of distinct entries if $A$ is a triangular matrix
$m =$ maximum number of distinct entries if $A$ is a diagonal matrix
$p =$ minimum number of zeroes if $A$ is a triangular matrix
If $l + 5 = p + 2 m$ , find the order of the matrix.

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