9 Let A Be A 2 X 2 Matrix With Real Entries Let I Be The 2 X 2 2identity Matrix Denote By T

Solved Consider An Arbitrary 2 X 2 Matrix With Real Entries Chegg To solve the problem, we need to analyze the given statements about the 2x2 matrix \ ( a \) such that \ ( a^2 = i \), where \ ( i \) is the identity matrix. ### step by step solution: 1. **matrix representation**: let \ ( a \) be represented as: \ [ a = \begin {pmatrix} a & b \\ c & d \end {pmatrix} \] 2. Let a be a 2× 2 matrix with real entries. let i be the 2 × 2 identity matrix. denote by tr (a), the sum of diagonal entries of a. assume that a2 = i . statement 1: if a ≠ i and a ≠ −i , then det a = − 1 . statement 2: if a ≠ i and a ≠ − i , then tr(a) ≠ 0 . text solution verified by experts.

Solved A Bn 9 Let A Be A 2x2 Matrix With Real Entries Chegg Let a be a 2×2 matrix with real entries. let i be the 2×2 identity matrix. denote by tr(a) the sum of the diagonal entries of a. assume that a2 = i. statement 1: if a = i and a = −i, then det(a) = −1. statement 2: if a = i and a =−i, then tr(a) =0. The trace of a matrix is the sum of its diagonal elements, and it reflects some of the intrinsic properties of the matrix's linear transformation. for our 2 × 2 matrix a, the trace is symbolized as tr (a). The trace of $a$ is $a d$. substituting the values we found for $a$ and $d$, we get $\operatorname {tr} (a) = \sqrt {1 bc} \sqrt {1 bc} = 0$. therefore, statement 2 is false. so, the final answer is $\boxed {\text { (d) statement 1 is true, statement 2 is false}}$. The correct statement should be: if a^2 = i, then tr (a) = 0 or tr (a) = 2. if a^2 = i, then (a^2 i) = 0. this can be factored as (a i) (a i) = 0. since matrix multiplication is not commutative, we cannot conclude that a i = 0 or a i = 0.

Let A Be A 2 2 Matrix With Real Entries Such That Sarthaks Econnect The trace of $a$ is $a d$. substituting the values we found for $a$ and $d$, we get $\operatorname {tr} (a) = \sqrt {1 bc} \sqrt {1 bc} = 0$. therefore, statement 2 is false. so, the final answer is $\boxed {\text { (d) statement 1 is true, statement 2 is false}}$. The correct statement should be: if a^2 = i, then tr (a) = 0 or tr (a) = 2. if a^2 = i, then (a^2 i) = 0. this can be factored as (a i) (a i) = 0. since matrix multiplication is not commutative, we cannot conclude that a i = 0 or a i = 0. Let a be a `2xx2` matrix with real entries. let i be the `2xx2` identity matrix. denote by tr (a) d. statement 1 is false, statement 2 is true. Solution let a be a 2 × 2 real matrix with entries from {0, 1} and |a| ≠ 0. consider the following two statements: (p) if a 1 i 2, then |a| = –1 (q) if |a| = 1, then tr (a) = 2, where i 2 denotes 2 × 2 identity matrix and tr (a) denotes the sum of the diagonal entries of a. then (p) is false and (q) is true. explanation: p: a = [1 0 1 0. 9, let a be a 2 x 2 matrix with real entries. let i be the 2 × 2 2identity matrix. denote by t. Let a be a 2 × 2 matrix with real entries let i be the 2 × 2 identity matrix. t r (a) denote by the sum of diagonal entries of a. assume that a 2 = i. statement 1: if a ≠ i and a ≠ i, then det (a) = 1.

Let A Be A 2 2 Matrix With Real Entries Such That Sarthaks Econnect Let a be a `2xx2` matrix with real entries. let i be the `2xx2` identity matrix. denote by tr (a) d. statement 1 is false, statement 2 is true. Solution let a be a 2 × 2 real matrix with entries from {0, 1} and |a| ≠ 0. consider the following two statements: (p) if a 1 i 2, then |a| = –1 (q) if |a| = 1, then tr (a) = 2, where i 2 denotes 2 × 2 identity matrix and tr (a) denotes the sum of the diagonal entries of a. then (p) is false and (q) is true. explanation: p: a = [1 0 1 0. 9, let a be a 2 x 2 matrix with real entries. let i be the 2 × 2 2identity matrix. denote by t. Let a be a 2 × 2 matrix with real entries let i be the 2 × 2 identity matrix. t r (a) denote by the sum of diagonal entries of a. assume that a 2 = i. statement 1: if a ≠ i and a ≠ i, then det (a) = 1.

Solved Consider An Arbitrary 2 2 Matrix With Real Entries A Chegg 9, let a be a 2 x 2 matrix with real entries. let i be the 2 × 2 2identity matrix. denote by t. Let a be a 2 × 2 matrix with real entries let i be the 2 × 2 identity matrix. t r (a) denote by the sum of diagonal entries of a. assume that a 2 = i. statement 1: if a ≠ i and a ≠ i, then det (a) = 1.