Advertisements
Advertisements
प्रश्न
Answer the following question:
Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`
उत्तर
Given equations are
2A – B = `[(1, -1),(0, 1)]` ....(i)
and A + 3B = `[(1, -1),(0, 1)]` ...(ii)
By (i) × 3 + (ii), we get
7A = `3[(1, -1),(0, 1)] + [(1, -1),(0, 1)]`
∴ 7A = `[(3, -3),(0, 3)] + [(1, -1),(0, 1)]`
∴ 7A = `[(4, -4),(0, 4)]`
∴ A = `1/7[(4, -4),(0, 4)]`
By (i) – (ii) × 2, we get
–7B = `[(1, -1),(0, 1)] -2[(1, -1),(0, 1)]`
= `[(1, -1),(0, 1)] - [(2, -2),(0, 2)]`
∴ –7B = `[(-1, 1),(0, -1)]`
∴ B = `- 1/7[(-1, 1),(0, -1)]`
∴ B = `1/7[(1, -1),(0, 1)]`
APPEARS IN
संबंधित प्रश्न
Simplify the following :
`{3 [(1,2,0),(0,-1,3)] - [(1,5,-2),(-3,-4,4)]} [(1),(2),(1)]`
If A = `[(5, 1, -4),(3, 2, 0)]`, find (AT)T.
Find a, b, c, if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
Find x, y, z if `[(0, -5i, x),(y, 0, z),(3/2, - sqrt(2), 0)]` is a skew symmetric matrix.
For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`
If [aij]3×3, where aij = 2(i – j), find A and AT. State whether A and AT both are symmetric or skew-symmetric matrices?
If A = `[(5, -3),(4, -3),(-2, 1)]`, prove that (AT)T = A.
If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, prove that AT = A.
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(2, 1),(4, -1),(-3, 3)], "C" = [(1, 2),(-1, 4),(-2, 3)]`, then show that (A + B)T = AT + BT.
If A = `[(5, 4),(-2, 3)]` and B = `[(-1, 3),(4, -1)]`, then find CT, such that 3A – 2B + C = I, whre I is e unit matrix of order 2.
Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(1, 2, 4),(3, 2, 1),(-2, -3, 2)]`
Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(5, 2, -4),(3, -7, 2),(4, -5, -3)]`
Express each of the following matrix as the sum of a symmetric and a skew symmetric matrix `[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`.
Choose the correct alternative.
If A = `[(α, 4),(4, α)]` and |A3| = 729, then α = ______.
State whether the following is True or False :
If A and B are square matrices of same order, then (A + B)2 = A2 + 2AB + B2.
Solve the following :
Find k, if `[(7, 3),(5, "k")]` is a singular matrix.
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2), (0, 3)] and "C" = [(4, 3),(-1, 4),(-2, 1)]` Show that A + B = B + A
If A = `[(1, -2),(3, -5),(-6, 0)], "B" = [(-1, -2),(4, 2),(1, 5)] and "C" = [(2, 4),(-1, -4),(-3, 6)]`, find the matrix X such that 3A – 4B + 5X = C.
Simplify, `costheta[(costheta, sintheta),(-sintheta, costheta)] + sintheta[(sintheta, -costheta),(costheta, sintheta)]`
Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] + [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`
There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.
July sales (in Rupees), Physics Chemistry Mathematics.
A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`
August sales(in Rupees), Physics Chemistry Mathematics
B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,
Find the increase in sales in Rupees from July to August 2017.
There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.
July sales (in Rupees), Physics Chemistry Mathematics.
A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`
August sales(in Rupees), Physics Chemistry Mathematics
B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,
If both book shops got 10 % profit in the month of August 2017, find the profit for each book seller in each subject in that month
Evaluate: `[(3),(2),(1)][(2,-4,3)]`
Evaluate : `[2 -1 3][(4),(3),(1)]`
Answer the following question:
Find matrices A and B, where 3A – B = `[(-1, 2, 1),(1, 0, 5)]` and A + 5B = `[(0, 0, 1),(-1, 0, 0)]`
Choose the correct alternative:
If A and B are two square matrices of order 3, then (AB)T = ______
State whether the following statement is True or False:
Every square matrix of order n can be expressed as sum of symmetric and skew symmetric matrix
State whether the following statement is True or False:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]` is a skew symmetric matrix
In a Skew symmetric matrix, all diagonal elements are ______
Find x, y, z if `{5[(0, 1),(1, 0),(1, 1)] - [(2, 1),(3, -2),(1, 3)]}[(2),(1)] = [(x + 1),(y - 1), (3z)]`
If `A = [(-3,2),(2,4)], B = [(1,a),(b,0)] "and" (A + B)(A-B) = A^2 - B^2, "Find" a "and" b`
If A = `[(5, 4),(-2, 3)]` and B = `[(-1, 3),(4, -1)]`, then find CT , such that 3A – 2B + C = I, where I is the unit matrix of order 2
