Advertisements
Advertisements
प्रश्न
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`
उत्तर
Given that,
2X + 3Y = `[(2, 3),(4, 0)]` ......(1)
3Y + 2Y = `[(-2, 2),(1, -5)]` ......(2)
Multiplying equation (1) by 3 and equaion (2) by 2, we get,
3[2X + 3Y] = `3[(2, 3),(4, 0)]`
⇒ 6X + 9Y = `[(6, 9),(12, 0)]` ....(3)
2[3X + 2Y] = `2[(-2, 2),(1, -5)]`
⇒ 6X + 4Y = `[(-4, 4),(2, -10)]` .....(4)
On subtracting eq. (4) from eq. (3) we get
5Y = `[(6 + 4, 9 - 4),(12 - 2, 0 + 10)]`
5Y = `[(10, 5),(10, 10)]`
⇒ Y = `[(2, 1),(2, 2)]`
Now, putting the value of Y in equation (1) we get,
`2"X" + 3 [(2, 1),(2, 2)] = [(2, 3),(4, 0)]`
⇒ `2"X" + [(6, 3),(6, 60)] = [(2, 3),(4, 0)]`
⇒ 2X = `[(2, 3),(4, 0)] - [(6, 3),(6, 6)]`
⇒ 2X = `[(2 - 6, 3 - 3),(4 - 6, 0 - 6)]`
⇒ 2X = `[(-4,0),(-2, -6)]`
⇒ = `1/2 [(-4, 0),(-2, -6)]`
⇒ X = `[(-2, 0),(-1, -3)]`
Hence, X = `[(-2, 0),(-1, -3)]` and Y = `[(2, 1),(2, 2)]`
APPEARS IN
संबंधित प्रश्न
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
if `A = [(0, -tan alpha/2), (tan alpha/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I -A)[(cos alpha, -sin alpha),(sin alpha, cos alpha)]`
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.
A coaching institute of English (subject) conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, it has 20 poor and 5 rich children and total monthly collection is Rs 9,000, whereas in batch II, it has 5 poor and 25 rich children and total monthly collection is Rs 26,000. Using matrix method, find monthly fees paid by each child of two types. What values the coaching institute is inculcating in the society?
Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.
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:
`[(3, -2, 4),(0, 0, -5),(0, 0, 0)]`
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)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Find k if the following matrix is singular:
`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix
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.
Answer the following question:
If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
If A is a square matrix, then A – A’ is a ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
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 ______.
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 ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
