Arts (English Medium) Class 12 - CBSE Important Questions

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?

Use elementary column operations  \[C_2 \to C_2 - 2 C_1\] in the matrix equation \[\begin{pmatrix}4 & 2 \\ 3 & 3\end{pmatrix} = \begin{pmatrix}1 & 2 \\ 0 & 3\end{pmatrix}\begin{pmatrix}2 & 0 \\ 1 & 1\end{pmatrix}\] .

If \[\begin{pmatrix}a + 4 & 3b \\ 8 & - 6\end{pmatrix} = \begin{pmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{pmatrix},\] ,write the value of a − 2b.

Two schools P and Q want to award their selected students on the values of tolerance, kindness and leadership. School P wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively, with a total award money of Rs 2,200. School Q wants to spend Rs 3,100 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each value is Rs 1,200, using matrices, find the award money for each value.

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

Using elementary row operations, find the inverse of the matrix A = `((3, 3,4),(2,-3,4),(0,-1,1))` and hence solve the following system of equations :  3x - 3y + 4z = 21, 2x -3y + 4z = 20, -y + z = 5.

If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.

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"]`

If A = [a_ij] is a skew-symmetric matrix of order n, then ______.

If A, B are non-singular square matrices of the same order, then (AB^–1)^–1 = ______.

Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.

If A = `[(5, x),(y, 0)]` and A = A^T, where A^T is the transpose of the matrix A, then ______.

If A and B are invertible square matrices of the same order, then which of the following is not correct?

The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R⁺, is ______.

If `|[2x,5],[8,x]|=|[6,-2],[7,3]|`, write the value of x.

Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z,z-x-y],[x-y-z,2x,2x]|=(x+y+z)^3`

Find the value of a if `[[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]`

If `|[x+1,x-1],[x-3,x+2]|=|[4,-1],[1,3]|`, then write the value of x.

Using properties of determinants prove the following: `|[1,x,x^2],[x^2,1,x],[x,x^2,1]|=(1-x^3)^2`