Advertisements
Advertisements
प्रश्न
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Advertisements
उत्तर
Let A = `[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Since A is a singular matrix,
|A| = 0
∴ `|(4, 3, 1),(7, "k", 1),(10, 9, 1)|` = 0
∴ 4(k – 9) – 3(7 – 10) + 1(63 – 10k) = 0
∴ 4k – 36 + 9 + 63 – 10k = 0
∴ –6k + 36 = 0
∴ 6k = 36
∴ k = 6
APPEARS IN
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.
If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix.
if `A = [(3,-4),(1,-1)]` then prove A"=` [(1+2n, -4n),(n, 1-2n)]` where n is any positive integer
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
If A = `[(α, β),(γ, -α)]` is such that A2 = I, then ______.
Given two matrices A and B
`A = [(1,-2,3),(1,4,1),(1,-3, 2)] and B = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`
find AB and use this result to solve the following system of equations:
x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
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?
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
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:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Identify the following matrix is singular or non-singular?
`[(7, 5),(-4, 7)]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
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.
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______
If two matrices A and B are of the same order, then 2A + B = B + 2A.
A square matrix A = [aij]nxn is called a diagonal matrix if aij = 0 for ____________.
If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
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,-5,8),(5,0,12),(-8,-12,0)]` is a ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
If all the elements are zero, then matrix is said to be
A = `[a_(ij)]_(m xx n)` is a square matrix, if
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 ______.
Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.
If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
What is the order of a row matrix with \[n\] columns?
A matrix where the number of rows equals the number of columns is called a:
Which elements form the diagonal of a square matrix?
What is the order of \[A=\begin{bmatrix}3&-1&0\\ \dfrac{3}{2}&3\sqrt{2}&1\\ 4&3&-1\end{bmatrix}\]?
Which condition holds for a diagonal matrix when \[i\ne j\]?
How is an identity matrix denoted when its order is \[n\]?
