If A = [-1112301-31],B=[214302121]. State whether AB = BA? Justify your answer.

If A = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)], "B" = [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`. State whether AB = BA? Justify your answer.

योग

AB = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)] [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`

= `[(-2 + 3 + 1, -1 + 0 + 2, -4 + 2 + 1),(4 + 9 + 0, 2 + 0 + 0, 8 + 6 + 0),(2 - 9 + 1, 1 - 0 + 2, 4 - 6 + 1)]`

∴ AB = `[(2, 1, -1),(13, 2, 14),(-6, 3, -1)]` ...(i)

BA = `[(2, 1, 4),(3, 0, 2),(1, 2, 1)][(-1, 1, 1),(2, 3, 0),(1, -3, 1)]`

= `[(-2 + 2 + 4, 2 + 3 - 12, 2 + 0 + 4),(-3 + 0 + 2, 3 + 0 - 6, 3 + 0 + 2),(-1 + 4 + 1, 1 + 6 - 3, 1 + 0 + 1)]`

∴ BA = `[(4, -7, 6),(-1, -3, 5),(4, 4, 2)]` ...(ii)

From (i) and (ii), we get

AB ≠ BA

shaalaa.com

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

अध्याय 4: Determinants and Matrices - Exercise 4.6 [पृष्ठ ९४]

अध्याय 4 Determinants and Matrices
Exercise 4.6 | Q 3 | पृष्ठ ९४

Show that AB = BA where,

A = `[(-2, 3, -1),(-1, 2, -1),(-6, 9, -4)], "B" = [(1, 3, -1),(2, 2, -1),(3, 0, -1)]`

If A = `[(4, 8),(-2, -4)]`, prove that A² = 0

Verify A(BC) = (AB)C of the following case:

A = `[(1, 0, 1),(2, 3, 0),(0, 4, 5)], "B" = [(2, -2),(-1, 1),(0, 3)] and "C" = [(3, 2, -1),(2, 0, -2)]`

Verify A(BC) = (AB)C of the following case:

A = `[(2, 4, 3),(-1, 3, 2)], "B" = [(2, -2),(3, 3),(-1, 1)], "C" = [(3, 1),(1, 3)]`

Verify that A(B + C) = AB + AC of the following matrix:

A = `[(1, -1, 3),(2, 3, 2)], "B" = [(1, 0),(-2, 3),(4, 3)], "C" = [(1, 2),(-2, 0),(4, -3)]`

If A = `[(1, -2),(5, 6)], "B" = [(3, -1),(3, 7)]`, Find AB - 2I, where I is unit matrix of order 2.

If A = `[(1, 2, 0),(5, 4, 2),(0, 7, -3)]`, find the product (A + I)(A − I)

A = `[(alpha, 0),(1, 1)], "B" = [(1, 0),(2, 1)]` find α, if A² = B.

If A = `[(3, 4),(-4, 3)] and "B" = [(2, 1),(-1, 2)]`, show that (A + B)(A – B) = A² – B²

Find matrix X such that AX = B, where A = `[(1, -2),(-2, 1)]` and B = `[(-3),(-1)]`

Find x, if `[(1, "x", 1)][(1, 2, 3),(4, 5, 6),(3, 2, 5)] [(1),(-2), (3)]` = 0

If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, show that `"A"^2=[(cos2alpha, sin2alpha),(-sin2alpha, cos2alpha)]`

If A = `[(1, 2),(3, 5)]` B = `[(0, 4),(2, -1)]`, show that AB ≠ BA, but |AB| = IAl·IBI

Select the correct option from the given alternatives:

If `[(5, 7),(x, 1),(2, 6)] - [(1, 2),(-3, 5),(2, y)] = [(4, 5),(4, -4),(0, 4)]` then __________

Select the correct option from the given alternatives:

If A + B = `[(7, 4),(8, 9)]` and A − B = `[(1, 2),(0, 3)]` then the value of A is _______

Select the correct option from the given alternatives:

If `[("x", 3"x" - "y"),("zx" + "z", 3"y" - "w")] = [(3, 2),(4, 7)]` then ______

Select the correct option from the given alternatives:

If A = `[(-2, 1),(0, 3)]` and f(x) = 2x² – 3x, then f(A) = ………