Advertisements
Advertisements
प्रश्न
Let `A = [(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`. Find `A^2 + AB + B^2`
उत्तर
`A = [(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`
`A^2 = A xx A = [(1, 0),(2, 1)] xx [(1, 0),(2, 1)]`
`=[(1 xx 1 + 0 xx 2, 1 xx 0 + 0 xx 1),(2 xx 1 + 1 xx 2, 2 xx 0 + 1 xx 1)] = [(1, 0),(4, 1)]`
`AB = A xx B = [(1, 0),(2, 1)] xx [(2, 3),(-1, 0)]`
`=[(1 xx 2 + 0 xx (-1), 1 xx 3 + 0 xx 0),(2 xx 2 + 1 xx (-1), 2 xx 3 + 1 xx 0)]`
`= [(2, 3),(3, 6)]`
`B^2 = B xx B = [(2, 3),(-1, 0)] xx [(2, 3),(-1, 0)]`
`= [(2 xx 2 + 3 xx (-1), 2 xx 3 + 3 xx 0),((-1)xx2 + 0 xx (-1), -1 xx 3 + 0 xx 0)]`
`= [(1, 6),(-2, -3)]`
`:. A^2 + AB + B^2 = [(1, 0),(4, 1)] + [(2, 3),(3, 6)] + [(1, 6),(-2, -3)]`
`= [(4, 9),(5, 4)]`
APPEARS IN
संबंधित प्रश्न
If A = `[(1, 3),(3, 4)]`, B = `[(-2, 1),(-3, 2)]` and A2 – 5B2 = 5C. Find matrix C where C is a 2 by 2 matrix.
Evaluate:
`[(4 sin 30°, 2 cos 60°),(sin 90°, 2 cos 0°)] [(4, 5),(5, 4)]`
If A = `[(1, 2),(2, 1)]` and B = `[(2, 1),(1, 2)]`; find (AB)B
If A = `|(1215),(1117)|` and B = `|(2,7),(4,9)|` find : 2A + 3B
If M = `|(8,3),(9,7),(4,3)|` and N = `|(4,7),(5,3),(10 , 1)|` find M+N
Find x, y if `[(-2, 0),(3, 1)] [(-1),(2x)] +3[(-2),(1)] = 2[(y),(3)]`.
Find X and Y, if
`[(2x, x),(y , 3y)][(3),(2)] = [(16),(9)]`
Find the value of x if `[(3x + y, -y),(2y - x, 3)] = [(1, 2),(-5, 3)]`
If B = `[(-4, 2),(5, -1)] and "C" = [(17, -1),(47, -13)]` find the matrix A such that AB = C
Choose the correct answer from the given four options :
If `x[(2),(3)] + y[(-1),(0)] = [(10),(6)]` then the values of x and y are
