Advertisements
Advertisements
प्रश्न
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
विकल्प
True
False
उत्तर
True
APPEARS IN
संबंधित प्रश्न
If A = `[(1,2),(3,-1)] , "B" = [(7,1),(2,5)]`
Verify that |AB| = |A|.|B|
Solve the following equations by reduclion method
x+3y+3z= 16 , x+4y+4z=21 , x+3y+4z = 19
If A = `[(2, 1), (1, 1)]` show that A2 - 3A + I = 0
Solve the following equations by reduction method :
x + 2y + z = 8
2x+ 3y - z = 11
3x - y - 2z = 5
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 = `[(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) + C = A + (B + C)
Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]` and X – 3Y = `[(0, -1),(0, -1)]`.
Find matrices A and B, if 2A – B = `[(6, -6, 0),(-4, 2, 1)]` and A – 2B = `[(3, 2, 8),(-2, 1, -7)]`.
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.
If A = `[(1, 2),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and (A + B)2 = A2 + B2, find the values of a and b.
Find AT, if A = `[(1, 3),(-4, 5)]`
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 = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find 5AT – 5BT.
If A = `[(-1, 2, 1),(-3, 2, -3)]` and B = `[(2, 1),(-3, 2),(-1, 3)]`, prove that (A + BT)T = AT + B.
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (AB)T = BTAT.
If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (BA)T = ATBT.
Choose the correct alternative.
If A = `[(α, 4),(4, α)]` and |A3| = 729, then α = ______.
Fill in the blank:
A = `[(3),(1)]` is ........................ matrix.
Fill in the blank :
If A = `[(4, x),(6, 3)]` is a singular matrix, then x is _______
Fill in the blank :
Matrix B = `[(0, 3, 1),(-3, 0, -4),("p", 4, 0)]` is skew symmetric, then the value of p is _______
Solve the following :
Find x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric matrix.
Find a, b, c if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` 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) + C = A + (B + C)
If A = `[("i", 2"i"),(-3, 2)] and "B" = [(2"i", "i"),(2, -3)]`, where `sqrt(-1)` = i,, find A + B and A – B. Show that A + B is a singular. Is A – B a singular ? Justify your answer.
Evaluate: `[(3),(2),(1)][(2,-4,3)]`
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 = `[(1, 3/5, x),(y, -5, -7),(-4, -7, 0)]` is a symmetric matrix, then the values of x and y are ______ respectively.
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`
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
