Let a determinant is given by `A=|[a,b,c],[p,q,r],[x,y,z]|` and suppose `det. A = 6.` lf `B=|[p+x,q+y,r+z],[a+x,b+y,c+z],[a+p,b+q,c+r]|` then find detB.

In the adjacent figure, find the value of x, y, z and a, b, c.

If A = [[a,b,c],[x,y,z],[p,q,r]], B= [[q , -b,y],[-p,a,-x],[r,-c,z]] and if A is invertible, then which of the following is not true?

A point P moves on a plane (x)/(a)+(y)/(b)+(z)/(c)=1 . A plane through P and perpendicular to OP meets the coordinate axes in A, B and C. If the planes throught A, B and C parallel to the planes x=0, y=0 and z=0 intersect in Q, then find the locus of Q.

If A={p,q,r} and B={q,p,r}. Then check whether A=B or not.

If the determinant |[a+p, l+x, u+f], [b+q, x+y, v+g], [c+r, n+z, w+h]| splits into exactly K determinants of order 3, each element of which contains only one term, then the values of K is

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

A plane meets the coordinate axes in A ,B ,C such that eh centroid of triangle A B C is the point (p ,q ,r)dot Show that the equation of the plane is x/p+y/q+z/r=3.

Find the value of a and b, given that p || q and r || s.

Using the property of determinants and without expanding prove the following |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

If A xx B={(,(p,q),(p,r)),(,(m,q),(m,r)):}} , find A and B.