Let A = beginpmatrix2 -2 1 -1 endpmatrix and B = beginpmatrix-1 2 -1 2 endpmatrix. Then the number of elements in the set ( n , m ): n , m ∈ 1,2, ldots ., 10 . and .nA n + mB m = I is

Question

Let A = beginpmatrix2 -2 1 -1 endpmatrix and B = beginpmatrix-1 2 -1 2 endpmatrix. Then the number of elements in the set ( n , m ): n , m ∈ 1,2, ldots ., 10 . and .nA n + mB m = I is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

A2=A and B2=B Therefore equation nA n + mB m = I becomes nA + mB = I, which gives m = n =1 Only one set possible

Q. Let $A = (21 - 2 - 1)$ and $B = (- 1 - 1 22)$ . Then the number of elements in the set ${(n, m) : n, m \in {1, 2, \dots ., 10}$ and $n A^{n} + m B^{m} = I}$ is____

$A^{2} = A$ and $B^{2} = B$
Therefore equation $n A^{n} + m B^{m} = I$ becomes $n A + m B = I$ , which gives $m = n = 1$
Only one set possible

Q. Let A=(21​−2−1​) and B=(−1−1​22​). Then the number of elements in the set {(n,m):n,m∈{1,2,….,10} and nAn+mBm=I} is____

A2=A and B2=B Therefore equation nAn+mBm=I becomes nA+mB=I, which gives m=n=1 Only one set possible

Q. Let $A = (21 - 2 - 1)$ and $B = (- 1 - 1 22)$ . Then the number of elements in the set ${(n, m) : n, m \in {1, 2, \dots ., 10}$ and $n A^{n} + m B^{m} = I}$ is____

$A^{2} = A$ and $B^{2} = B$
Therefore equation $n A^{n} + m B^{m} = I$ becomes $n A + m B = I$ , which gives $m = n = 1$
Only one set possible