Find the Rank [[3,x,-4],[4,2,1],[0,-4,5]]=6

Problem

Rank*[[3,x,−4],[4,2,1],[0,−4,5]]=6

Solution

1. Analyze the dimensions of the matrix. The given matrix is a 3×3 matrix.

2. Identify the maximum possible rank. The rank of a matrix cannot exceed the number of its rows or columns.

3. Compare the required rank to the maximum possible rank. For a 3×3 matrix, the maximum possible rank is 3

4. Conclude that the statement is impossible. Since 6>3 there is no value of x that can make the rank of this matrix equal to 6

Final Answer

No solution exists because the maximum rank of a *3×3* matrix is *3.

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