Advertisements
Advertisements
प्रश्न
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C
Advertisements
उत्तर
A = diag [2 –3 –5]
∴ A = `[(2, 0, 0),(0, -3, 0),(0, 0, -5)]`
B = diag [4 –6 –3]
∴ B = `[(4, 0, 0),(0, -6, 0),(0, 0, -3)]`
C = diag [–3 4 1]
∴ C = `[(-3, 0, 0),(0, 4, 0),(0, 0, 1)]`
2A + B – 5C = 2 diag [2 – 3 – 5] + diag [4 – 6 – 3] – 5 diag [ –3 4 1]
`= 2[(2, 0, 0),(0, -3, 0),(0, 0, -5)] + [(4, 0, 0),(0, -6, 0),(0, 0, -3)] -5[(-3, 0, 0),(0, 4, 0),(0, 0, 1)]`
`= [(4, 0, 0),(0, -6, 0),(0, 0, -10)] + [(4, 0, 0),(0, -6, 0),(0, 0, -3)] - [(-15, 0, 0),(0, 20, 0),(0, 0, 5)]`
`= [(4 + 4 - (-15), 0, 0),(0, -6 - 6 - 20, 0),(0, 0, -10 - 3 - 5)]`
`= [(23, 0, 0),(0, -32, 0),(0, 0, -18)]`
= diag [23 – 32 – 18].
APPEARS IN
संबंधित प्रश्न
Find the value of x, y, and z from the following equation:
`[(4,3),(x,5)] = [(y,z),(1,5)]`
Find the value of x, y, and z from the following equation:
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`
If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
Choose the correct alternative.
The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(5),(4),(-3)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(6, 0),(0, 6)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.
If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.
Select the correct option from the given alternatives:
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A
Answer the following question:
If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.
Choose the correct alternative:
If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______
State whether the following statement is True or False:
If A is non singular, then |A| = 0
State whether the following statement is True or False:
If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1
State whether the following statement is True or False:
If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2
For the non singular matrix A, (A′)–1 = (A–1)′.
AB = AC ⇒ B = C for any three matrices of same order.
Show by an example that for A ≠ O, B ≠ O, AB = O
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]` is a ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
If all the elements are zero, then matrix is said to be
The number of all possible matrices of order 3/3, with each entry 0 or 1 is
Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0
If the sides a, b, c of ΔABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and `|(a^2, (s - a)^2, (s - a)^2),((s - b)^2, b^2, (s - b)^2),((s - c)^2, (s - c)^2, c^2)| = p^2/q` where p and q are co-prime and s is semiperimeter of ΔABC, then the value of (p – q) is ______.
The minimum number of zeros in an upper triangular matrix will be ______.
How many matrices can be obtained by using one or more numbers from four given numbers?
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
Let A = `[(0, -2),(2, 0)]`. If M and N are two matrices given by M = `sum_(k = 1)^10 A^(2k)` and N = `sum_(k = 1)^10 A^(2k - 1)` then MN2 is ______.
If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.
