If a1b1,c1,a2b2c2anda3b3c3 are three digit even natural numbers and =∣c1a1b1c2a2b2c3a3b3∣,thenis divisible by 2 but not necessarily by 4 divisible by 4 but not necessarily by 8 divisible by 8 none of these
Without expanding show that
If =∣∣s∫hηcosφsinθs∈φcosθcosθcosφcosθs∈φ−s∫hη−s∫hηs∈φs∫hηcosφ0∣∣ then is independent of θ is independent of φ Delta is a constant (dthηdDelta])θ=π/2=0
Consider the system of the equation kx+y+z=1,x+ky+z=k,andx+y+kz=k2˙ Statement 1: System equations has infinite solutions when k=1. Statement 2: If the determinant ∣∣111kk1k21k∣∣=0, t hen k=−1.
For what values of k, does the system of linear equation x+y+z=2, 2x+y−z=3, 3x+2y+kz=4 have a unique solution?