Advertisements
Advertisements
प्रश्न
If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]`, then find the matrix A – 2B + 6I, where I is the unit matrix of order 2.
उत्तर
A – 2B + 6I = `[(1, -2),(5, 3)] - 2[(1, -3),(4, -7)] + 6[(1, 0),(0, 1)]`
= `[(1, -2),(5, 3)] - [(2, -6),(8, -14)] + [(6, 0),(0, 6)]`
= `[(1 - 2 + 6, -2 + 6 + 0),(5 - 8 + 0, 3 + 14 + 6)]`
= `[(5, 4),(-3, 23)]`
APPEARS IN
संबंधित प्रश्न
Find x and y if `x + y = [(7,0),(2,5)] , x - y[(3,0),(0,3)]`
Solve the following equations by reduclion method
x+3y+3z= 16 , x+4y+4z=21 , x+3y+4z = 19
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` ,
verify that A (adj A) = (adj A) A = |A| . I
Solve the following equations by reduction method :
x + 2y + z = 8
2x+ 3y - z = 11
3x - y - 2z = 5
If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]` , then find the matrix A − 2B + 6I, where I is the unit matrix of order 2.
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, find (AT)T.
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.
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]` and X – 3Y = `[(0, -1),(0, -1)]`.
If `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.
There are two book shops own 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)][("Suresh"), ("Ganesh")]`
August Sales (in Rupees) Physics Chemistry Mathematics
B = `[(6650, 7055, 8905),(7000, 7500, 10200)][("Suresh"), ("Ganesh")]`
Find the increase in sales in Rupees from July to August 2017.
Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`
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)]`.
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (AB)T = BTAT.
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 is symmetric, then A = –AT.
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 x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric 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
Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] + [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`
Evaluate: `[(3),(2),(1)][(2,-4,3)]`
Answer the following question:
If A = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, B = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, show that BA = 6I
Choose the correct alternative:
If A = `[(1, 3/5, x),(y, -5, -7),(-4, -7, 0)]` is a symmetric matrix, then the values of x and y are ______ respectively.
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
In a Skew symmetric matrix, all diagonal elements are ______
Find k, if A = `[(3, -2),(4, -2)]` and A2 = kA – 2I, where I is identity matrix of order 2
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 = `[(2, 5),(1, 3)]` then A–1 = ______.
If `A = [(-3,2),(2,4)], B = [(1,a),(b,0)] "and" (A + B)(A-B) = A^2 - B^2, "Find" a "and" b`
Find the x, y, z, if `{3[(2,0),(0,2),(2,2)]-4[(1,1),(-1,2),(3,1)]}[(1),(2)]=[(x-3),(y-1),( 2z)]`
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