Advertisements
Advertisements
Question
Fill in the blank:
A = `[(3),(1)]` is ........................ matrix.
Solution
A = `[(3),(1)]` is Column matrix.
APPEARS IN
RELATED QUESTIONS
Solve the following equations by reduction method:
x + y + z = 6,
3x - y + 3z = 10
5x + y - 4z = 3
If A = `[(1,2),(3,-1)] , "B" = [(7,1),(2,5)]`
Verify that |AB| = |A|.|B|
Simplify the following :
`{3 [(1,2,0),(0,-1,3)] - [(1,5,-2),(-3,-4,4)]} [(1),(2),(1)]`
If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.
Solve the following equations by reduction method :
x + 2y + z = 8
2x+ 3y - z = 11
3x - y - 2z = 5
A computers centre has four expert programmers . The centre needs four application programmes to be developed. The head of the computer centre , after stying carefully the programmes to be developed , estimates the computer time in minutes required by the respective experts to develop the application programmes as follows :
Programmes | ||||
Programmes | 1 | 2 | 3 | 4 |
(Times in minutes) | ||||
A | 120 | 100 | 80 | 90 |
B | 80 | 90 | 110 | 70 |
C | 110 | 140 | 120 | 100 |
D | 90 | 90 | 80 | 90 |
How should the head of the computer centre assign the programmes to the programmers so that the total time required is minimum ?
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.
Find a, b, c, if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.
Find matrices A and B, if 2A – B = `[(6, -6, 0),(-4, 2, 1)]` and A – 2B = `[(3, 2, 8),(-2, 1, -7)]`.
Find AT, if A = `[(2, -6, 1),(-4, 0, 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 = `[(2, -3),(5, -4),(-6, 1)], "B" = [(2, 1),(4, -1),(-3, 3)], "C" = [(1, 2),(-1, 4),(-2, 3)]`, then show that (A – C)T = AT – CT.
If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find 5AT – 5BT.
If A = `[(1, 0, 1),(3, 1, 2)], "B" = [(2, 1, -4),(3, 5, -2)] "and" "C" = [(0, 2, 3),(-1, -1, 0)]`, verify that (A + 2B + 3C)T = AT + 2BT + CT.
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)]`
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.
The matrix `[(0, 0, 0),(0, 0, 0)]` 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 _______
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 k, if `[(7, 3),(5, "k")]` is a singular matrix.
Solve the following :
Find x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric matrix.
If A = `[(1, 2, -3),(-3, 7, -8),(0, -6, 1)], "B" = [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]` then find the matrix C such that A + B + C is a zero matrix
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.
Find matrices A and B, if `2"A" - "B" = [(6, -6, 0),(-4, 2, 1)] and "A" - 2"B" = [(3, 2, 8),(-2, 1, -7)]`
Simplify, `costheta[(costheta, sintheta),(-sintheta, costheta)] + sintheta[(sintheta, -costheta),(costheta, sintheta)]`
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.
Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] + [(-1, 6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`
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 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.
Answer the following question:
Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`
Choose the correct alternative:
`[(3, 2, 1)][(2),(-2),(-1)]` = ______
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 ______
If A = `[(2, 5),(1, 3)]` then A–1 = ______.
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)]`