Advertisements
Advertisements
प्रश्न
Find the value of a, b, c, and d from the equation:
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
Advertisements
उत्तर
`[(a-b, 2a+c),(2a-b, 3x+d)] = [(-1,5),(0,13)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get:
a − b = −1 ....(1)
2a − b = 0 ....(2)
2a + c = 5 ....(3)
3c + d = 13 ...(4)
From (2), we have:
b = 2a
Then, from (1), we have:
a − 2a = −1
⇒ a = 1
⇒ b = 2
Now, from (3), we have:
2 ×1 + c = 5
⇒ c = 3
From (4) we have:
3 ×3 + d = 13
⇒ 9 + d = 13
⇒ d = 4
∴ a = 1, b = 2, c = 3, and d = 4
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)]`
Find the value of x, y, and z from the following equation:
`[(x+y+z), (x+z), (y+z)] = [(9),(5),(7)]`
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 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 the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'
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?
Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
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.
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
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:
`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`
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:
`[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
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, 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.
If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2
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
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
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
If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______
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)]`
For any square matrix A, AAT is a ____________.
`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠ 0. Consider the following two statements:
(P) If A1I2, then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,
where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then ______.
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 = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.
