If `[[2,-1],[1,0],[-3,4]]A=[[-1,-8,-10],[1,-2,-5],[9,22,15]]` , then sum of all the elements of matrix `A` is

If [(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)] , find A.

A is a 2xx2 matrix such that A[[1],[-1]]=[[-1],[ 2]] and A^2[[1],[-1]]=[[1],[ 0]]dot The sum of the elements of A is a. -1 b. 0 c. 2 d. 5

Let A=[(1,1,1),(1,-1,0),(0,1,-1)], A_(1) be a matrix formed by the cofactors of the elements of the matrix A and A_(2) be a matrix formed by the cofactors of the elements of matrix A_(1) . Similarly, If A_(10) be a matrrix formed by the cofactors of the elements of matrix A_(9) , then the value of |A_(10)| is

If [(9,-1,4),(-2,1,3)]=A+[(1,2,-1),(0,4,9)], then find the matrix A.

Express the matrix A=[[3,-2,-4], [3,-2,-5],[-1, 1, 2]] as the sum of a symmetric and skew-symmetric matrix and verify your result.

Find the rank of matrix A= [[1,2,-1,0],[0,1,3,1],[2,5,1,2]]

If A is a square matrix of order 2 such that A[(,1),(,-1)]=[(,-1),(,2)] and A^(2)[(,1),(,-1)]=[(,1),(,0)] the sum of elements and product of elements of A are S and P, S + P is

Express the matrix B=[[2,-2,-4],[-1, 3,4],[ 1,-2,-3]] as the sum of a symmetric and skew symmetric matrix.

Find the matrix A such that [{:(2,-1), (1,0),(-3,4):}]A=[{:(-1,-8,-10),(1,-2,-5),(9,22,15):}]

If A is a square matrix of any order then |A-x|=0 is called the chracteristic equation of matrix A and every square matrix satisfies its chatacteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-x)]=[(1-x,2),(1,5-x)] Characteristic equation of matrix A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x)(0-2)=0 or x^2-6x+3=0 Matrix A will satisfy this equation ie. A^2-6A+3I=0 . A^-1 can be determined by multiplying both sides of this equation. Let A=[(1,0,0),(0,1,1),(1,-2,4)] On the basis for above information answer the following questions:Sum of elements of A^-1 is (A) 2 (B) -2 (C) 6 (D) none of these