If for two matrices M and N, N = and product M × N = [-1 4]; find matrix M.

Let order of matrix M be a × b. 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. ∴ b = 2 Also, the no. of rows of product (resulting) matrix is equal to no. of rows of first matrix. ∴ a = 1 Order of matrix M = a × b = 1 × 2. Let M = . By definition of equality of matrices we get, ⇒ 3x + 2y = -1 and 2x - y = 4 From 2x - y = 4 ⇒ y = 2x - 4 Substituting value of y in 3x + 2y = -1 ⇒ 3x + 2(2x - 4) = -1 ⇒ 3x + 4x - 8 = -1 ⇒ 7x = -1 + 8 ⇒ 7x = 7 ⇒ x = 1. ⇒ y = 2x - 4 = 2(1) - 4 = 2 - 4 = -2. ∴ M = . Hence, M =

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

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The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

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If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

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If a, b, c are in A.P., show that : (b + c), (c + a) and (a + b) are also in A.P.

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Mathematics

If for two matrices M and N, N = and product M × N = [-1 4]; find matrix M.

Matrices

Related Questions

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

If a, b, c are in A.P., show that : (b + c), (c + a) and (a + b) are also in A.P.

Mathematics

If for two matrices M and N, N = and product M × N = [-1 4]; find matrix M.

Matrices

Related Questions

What number should be subtracted from 2x3 - 5x2 + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

The expression 4x3 - bx2 + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.

If the sum of first 20 terms of an A.P. is same as the sum of its first 28 terms, find the sum of its 48 terms.

If a, b, c are in A.P., show that : (b + c), (c + a) and (a + b) are also in A.P.

What number should be subtracted from 2x³ - 5x² + 5x + 8 so that the resulting polynomial has a factor 2x - 3 ?

The expression 4x³ - bx² + x - c leaves remainder 0 and 30 when divided by (x + 1) and (2x - 3) respectively. Calculate the values of b and c.