मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

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: [2003-10-731] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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)]`

बेरीज

उत्तर

Let A = `[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]`

As every element above the diagonal is zero in matrix A.

∴ A is a lower triangular matrix.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Determinants and Matrices - Exercise 4.4 [पृष्ठ ८३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 4 Determinants and Matrices
Exercise 4.4 | Q 2. (vi) | पृष्ठ ८३

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.


`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.


Find the matrix X so that  X`[(1,2,3),(4,5,6)]= [(-7,-8,-9),(2,4,6)]`


Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.


if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'


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)]`

 


If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| . 


If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.


Identify the following matrix is singular or non-singular?

`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`


If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`


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 _______


Select the correct option from the given alternatives:

If A and B are square matrices of equal order, then which one is correct among the following?


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


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 and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2 


If two matrices A and B are of the same order, then 2A + B = B + 2A.


For the non singular matrix A, (A′)–1 = (A–1)′.


If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2 


Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′? 


If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.


For any square matrix A, AAT is a ____________.


If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.


If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.


If a matrix A is both symmetric and skew-symmetric, then ____________.


The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.


The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]`  is a ____________.


`root(3)(4663) + 349` = ? ÷ 21.003


`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?


A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are


A diagonal matrix is said to be a scalar matrix if its diagonal elements are


If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to


If D = `[(0, aα^2, aβ^2),(bα + c, 0, aγ^2),(bβ + c, (bγ + c), 0)]` is a skew-symmetric matrix (where α, β, γ are distinct) and the value of `|((a + 1)^2, (1 - a), (2 - c)),((3 + c), (b + 2)^2, (b + 1)^2),((3 - b)^2, b^2, (c + 3))|` is λ then the value of |10λ| is ______.


If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.


If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.


A matrix which is both symmetric and skew symmetric matrix is a ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×