TIFR-2011-Maths-B-13

Question

Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.

Answer 1

let k=2 such that "ad-bc not equal to zero" that is" ad not equal to bc"  concider 2.3 not equal to 3.5 now if replace 2 by 5 they become equal that is determinant is zero.so above statement is true