Find matrix B, if matrix A = , matrix C = and AB = 3C.

Let order of matrix B = m × n Given, AB = 3C Since, the product of matrices is possible, only when the number of columns in the first matrix is equal to the number of rows in the second. ∴ m = 2 Also, the no. of columns of product (resulting) matrix is equal to no. of columns of second matrix. ∴ n = 1 Order of matrix B = m × n = 2 × 1. Let matrix B = Substituting matrix in AB = 3C we get, ∴ a + 5b = 6 ........(1) a + 2b = 3 ........(2) Subtracting equation (2) from (1), we get : ⇒ a + 5b - (a + 2b) = 6 - 3 ⇒ a - a + 5b - 2b = 3 ⇒ 3b = 3 ⇒ b = 1. Substituting value of b in (1), we get : ⇒ a + 5(1) = 6 ⇒ a + 5 = 6 ⇒ a = 1. B = Hence, B = .

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

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Let R₁ and R₂ are remainders when the polynomial x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R₁ + R₂ = 6; find the value of a.

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Mathematics

Find matrix B, if matrix A = , matrix C = and AB = 3C.

Matrices

Related Questions

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

Let R₁ and R₂ are remainders when the polynomial x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R₁ + R₂ = 6; find the value of a.

Mathematics

Find matrix B, if matrix A = , matrix C = and AB = 3C.

Matrices

Related Questions

What number should be added to x3 - 9x2 - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

Let R1 and R2 are remainders when the polynomial x3 + 2x2 - 5ax - 7 and x3 + ax2 - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R1 + R2 = 6; find the value of a.

What number should be added to x³ - 9x² - 2x + 3 so that the remainder may be 5 when divided by (x - 2) ?

Let R₁ and R₂ are remainders when the polynomial x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by (x + 1) and (x - 2) respectively. If 2R₁ + R₂ = 6; find the value of a.