Using the properties of determinants, evalulate `|(23,6,11),(36,5,26),(63,13,37)|`

Using the properties of detminants, evalulate. (i) |{:(,23,6,11),(,36,5,26),(,63,13,37):}| (ii) |{:(,sqrt13+sqrt3,2sqrt5,sqrt5),(,sqrt15+sqrt26,5,sqrt10),(,3+sqrt65,sqrt15,5):}|

Using the properties of detminants, evalulate. (i) |{:(,23,6,11),(,36,5,26),(,63,13,37):}| (ii) |{:(,sqrt13+sqrt3,2sqrt5,sqrt5),(,sqrt15+sqrt26,5,sqrt10),(,3+sqrt65,sqrt15,5):}|

Use properties of determinants to evaluate : |{:(102,18,36),(1,3,4),(17,3,6):}|

Using properties of determinants, prove that, |{:(1,1+p,1+p+q),(2,3+2p,1+3p+2q),(3,6+3p,1+6p+3q):}|=1

Using the property of determinants prove that {:|( 1,1+p,1+p+q),( 2,3+2p,1+3p+2q),( 3,6+3p,1+6p+3q)|:}=1

Without expanding show that : |(23,12,11),(36,10,26),(63,26,37)|=0

Using properties of determinants, prove that |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]| = 1

Using properties of determinants, prove the following: |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=1

Using properties of determinants in Exercise 11 to 15 prove that |{:(1,1+p,1+p+q),(2,3+2p,4+3p+2q),(3,6+3p,10+6p+3q):}|=1

Using the property of determinants and without expanding prove the following |{:(1,3,5),(2,6,10),(31,11,38):}|=0