For a real number α, if the system ⎣⎡1αα2α1αα2α1⎦⎤⎣⎡xyz⎦⎤=⎣⎡1−11⎦⎤ of linear equations, has infinitely many solutions, then 1+α+α2=
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If A1B1C1,A2B2C2andA3B3C3 are three digit numbers, each of which is divisible by k, then Δ=∣∣A1A2A3B1B2B3C1C2C3∣∣ is
, then f(x)
is a polynomial of degree
Show that :
Evaluate: (i) ∣∣x2+xy+y2x2−xy+y2x+yx−y∣∣ (ii) ∣∣1(log)ab(log)ba1∣∣
by two methods.
If the entries in a 3×3 determinant are either 0 or 1, then the greatest value of their determinants is
Show that the determinant
is always non-negative. When is the determinant zero?
Show that ∣∣aa2bcbb2cacc2ab∣∣=∣∣1a2a31b2b31c2c3∣∣=(a−b)(b−c)(c−a)(ab+bc+ca)