1. Consider the three vectors, u and v are 10 degrees above and below the x-axis...

1. Consider the three vectors, u and v are 10 degrees above and below the x-axis respectively, and ||u|| = 1, ||v|| = 2, and ||w|| = 3. Arrange the dot products taken among these vectors from least to greatest

2. Let A be a 4 x 6 matrix. Find the elimination matrix E that corresponds with the row operation "switch rows 1 and 3, and scale row 4 by a factor of 6.

3. Find the formula for the entry in the ith row and j column of the product AB in terms of the entries of A and B. Assume A is m x n and B is n x p.

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Expert Solution

part(2) we have given that A is 4 by 6 matrix

suppose it looks like A=

we have to find the elimination matrix E by two operation that we have given are (i)switch rows 1 and 3(means you have to innterchange row 1 and 3)

(ii) scale row 4 by a factor of 6(multiply row 4 by 6)

then A=

part(3) here we have A is m by n matrix and B is n by p matrix

then AB will be an matrix of order m by p

then entries in the ith row=C_i₁ where i=1 to m for first column and where C_i1=A_inB_n1

C_i2 for second column and similarly C_ip for the p column

and formula for the column of the matrix=C_1i for first row where i= 1 to p

milcah answered 1 year ago

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